parameters.prm

# Listing of Parameters
# ---------------------
# A list of names of additional shared libraries that should be loaded upon
# starting up the program. The names of these files can contain absolute or
# relative paths (relative to the directory in which you call ASPECT). In
# fact, file names that do not contain any directory information (i.e., only
# the name of a file such as <myplugin.so> will not be found if they are not
# located in one of the directories listed in the \texttt{LD_LIBRARY_PATH}
# environment variable. In order to load a library in the current directory,
# use <./myplugin.so> instead.
# 
# The typical use of this parameter is so that you can implement additional
# plugins in your own directories, rather than in the ASPECT source
# directories. You can then simply compile these plugins into a shared library
# without having to re-compile all of ASPECT. See the section of the manual
# discussing writing extensions for more information on how to compile
# additional files into a shared library.
set Additional shared libraries                = /home/staff/agrima/aspect/release_210316/prescribed_velocity_pressure_plugin/libprescribed_velocity_pressure.so # default: 

# In order to make the problem in the first time step easier to solve, we need
# a reasonable guess for the temperature and pressure. To obtain it, we use an
# adiabatic pressure and temperature field. This parameter describes what the
# `adiabatic' temperature would be at the surface of the domain (i.e. at depth
# zero). Note that this value need not coincide with the boundary condition
# posed at this point. Rather, the boundary condition may differ significantly
# from the adiabatic value, and then typically induce a thermal boundary
# layer.
# 
# For more information, see the section in the manual that discusses the
# general mathematical model.
set Adiabatic surface temperature              = 0.

# In computations, the time step $k$ is chosen according to $k = c \min_K
# \frac {h_K} {\|u\|_{\infty,K} p_T}$ where $h_K$ is the diameter of cell $K$,
# and the denominator is the maximal magnitude of the velocity on cell $K$
# times the polynomial degree $p_T$ of the temperature discretization. The
# dimensionless constant $c$ is called the CFL number in this program. For
# time discretizations that have explicit components, $c$ must be less than a
# constant that depends on the details of the time discretization and that is
# no larger than one. On the other hand, for implicit discretizations such as
# the one chosen here, one can choose the time step as large as one wants (in
# particular, one can choose $c>1$) though a CFL number significantly larger
# than one will yield rather diffusive solutions. Units: None.
set CFL number                                 = 1.0

# The number of space dimensions you want to run this program in. ASPECT can
# run in 2 and 3 space dimensions.
set Dimension                                  = 2

# The end time of the simulation. The default value is a number so that when
# converted from years to seconds it is approximately equal to the largest
# number representable in floating point arithmetic. For all practical
# purposes, this equals infinity. Units: Years if the 'Use years in output
# instead of seconds' parameter is set; seconds otherwise.
set End time                                   = 2.4e8                                                                                                           # default: 5.69e+300

# The maximal number of nonlinear iterations to be performed.
set Max nonlinear iterations                   = 10

# The maximal number of nonlinear iterations to be performed in the
# pre-refinement steps. This does not include the last refinement step before
# moving to timestep 1. When this parameter has a larger value than max
# nonlinear iterations, the latter is used.
set Max nonlinear iterations in pre-refinement = 2147483647

# Set a maximum time step size for only the first timestep. Generally the time
# step based on the CFL number should be sufficient, but for complicated
# models or benchmarking it may be useful to limit the first time step to some
# value, especially when using the free surface, which needs to settle to
# prevent instabilities. This should in that case be combined with a value set
# for ``Maximum relative increase in time step''. The default value is a value
# so that when converted from years into seconds it equals the largest number
# representable by a floating point number, implying an unlimited time step.
# Units: Years or seconds, depending on the ``Use years in output instead of
# seconds'' parameter.
set Maximum first time step                    = 5.69e+300

# Set a percentage with which the the time step is limited to increase.
# Generally the time step based on the CFL number should be sufficient, but
# for complicated models which may suddenly drastically change behavior, it
# may be useful to limit the increase in the time step, without limiting the
# time step size of the whole simulation to a particular number. For example,
# if this parameter is set to $50$, then that means that the time step can at
# most increase by 50\% from one time step to the next, or by a factor of 1.5.
# Units: \%.
set Maximum relative increase in time step     = 2147483647

# Set a maximum time step size for the solver to use. Generally the time step
# based on the CFL number should be sufficient, but for complicated models or
# benchmarking it may be useful to limit the time step to some value. The
# default value is a value so that when converted from years into seconds it
# equals the largest number representable by a floating point number, implying
# an unlimited time step.Units: Years or seconds, depending on the ``Use years
# in output instead of seconds'' parameter.
set Maximum time step                          = 5.69e+300

# The kind of scheme used to resolve the nonlinearity in the system. `single
# Advection, single Stokes' means that no nonlinear iterations are done, and
# the temperature, compositional fields and Stokes equations are solved
# exactly once per time step, one after the other. The `iterated Advection and
# Stokes' scheme iterates this decoupled approach by alternating the solution
# of the temperature, composition and Stokes systems. The `single Advection,
# iterated Stokes' scheme solves the temperature and composition equation once
# at the beginning of each time step and then iterates out the solution of the
# Stokes equation. The `no Advection, iterated Stokes' scheme only solves the
# Stokes system, iterating out the solution, and ignores compositions and the
# temperature equation (careful, the material model must not depend on the
# temperature or composition; this is mostly useful for Stokes benchmarks).
# The `no Advection, single Stokes' scheme only solves the Stokes system once
# per timestep. This is also mostly useful for Stokes benchmarks. The `single
# Advection, no Stokes' scheme only solves the temperature and other advection
# systems once, and instead of solving for the Stokes system, a prescribed
# velocity and pressure is used. The `iterated Advection and Newton Stokes'
# scheme iterates by alternating the solution of the temperature, composition
# and Stokes equations, using Picard iterations for the temperature and
# composition, and Newton iterations for the Stokes system. The `single
# Advection, iterated Newton Stokes' scheme solves the temperature and
# composition equations once at the beginning of each time step and then
# iterates out the solution of the Stokes equation, using Newton iterations
# for the Stokes system. The `iterated Advection and defect correction Stokes'
# scheme iterates by alternating the solution of the temperature, composition
# and Stokes equations, using Picard iterations for the temperature and
# composition, and defect correction Picard iterations for the Stokes system.
# The `single Advection, iterated defect correction Stokes' scheme solves the
# temperature and composition equations once at the beginning of each time
# step and then iterates out the solution of the Stokes equation, using defect
# correction Picard iterations for the Stokes system. The `no Advection,
# iterated defect correction Stokes' scheme solves the temperature and
# composition equations once at the beginning of each time step and then
# iterates out the solution of the Stokes equation, using defect correction
# Picard iterations for the Stokes system. The `first timestep only, single
# Stokes' scheme solves the Stokes equations exactly once, at the first time
# step. No nonlinear iterations are done, and the temperature and composition
# systems are not solved.
# 
# The `IMPES' scheme is deprecated and only allowed for reasons of backwards
# compatibility. It is the same as `single Advection, single Stokes' .The
# `iterated IMPES' scheme is deprecated and only allowed for reasons of
# backwards compatibility. It is the same as `iterated Advection and Stokes'.
# The `iterated Stokes' scheme is deprecated and only allowed for reasons of
# backwards compatibility. It is the same as `single Advection, iterated
# Stokes'. The `Stokes only' scheme is deprecated and only allowed for reasons
# of backwards compatibility. It is the same as `no Advection, iterated
# Stokes'. The `Advection only' scheme is deprecated and only allowed for
# reasons of backwards compatibility. It is the same as `single Advection, no
# Stokes'. The `Newton Stokes' scheme is deprecated and only allowed for
# reasons of backwards compatibility. It is the same as `iterated Advection
# and Newton Stokes'.
set Nonlinear solver scheme                    = single Advection, single Stokes

# A relative tolerance up to which the nonlinear solver will iterate. This
# parameter is only relevant if the `Nonlinear solver scheme' does nonlinear
# iterations, in other words, if it is set to something other than `single
# Advection, single Stokes' or `single Advection, no Stokes'.
set Nonlinear solver tolerance                 = 1e-5

# The name of the directory into which all output files should be placed. This
# may be an absolute or a relative path.
set Output directory                           = outputs/MR_RG_VK_case9_AGG                                                                                      # default: output

# Whether or not to use any prescribed internal pressure. Locations in which
# to prescribe internal pressure are defined in section ``Prescribed
# fields/Pressure indicator function'' and the pressure is defined in section
# ``Prescribed fields/Pressure function''.
set Prescribe internal pressure                = true                                                                                                            # default: false

# Whether or not to use any prescribed internal velocities. Locations in which
# to prescribe velocities are defined in section ``Prescribed fields/Velocity
# indicator function'' and the velocities are defined in section ``Prescribed
# fields/Velocity function''. Indicators are evaluated at the center of each
# cell, and all DOFs associated with the specified velocity component at the
# indicated cells are constrained.
set Prescribe internal velocities              = true                                                                                                            # default: false

# If and how to normalize the pressure after the solution step. This is
# necessary because depending on boundary conditions, in many cases the
# pressure is only determined by the model up to a constant. On the other
# hand, we often would like to have a well-determined pressure, for example
# for table lookups of material properties in models or for comparing
# solutions. If the given value is `surface', then normalization at the end of
# each time steps adds a constant value to the pressure in such a way that the
# average pressure at the surface of the domain is what is set in the `Surface
# pressure' parameter; the surface of the domain is determined by asking the
# geometry model whether a particular face of the geometry has a zero or small
# `depth'. If the value of this parameter is `volume' then the pressure is
# normalized so that the domain average is zero. If `no' is given, the no
# pressure normalization is performed.
set Pressure normalization                     = no                                                                                                              # default: surface

# A flag indicating whether the computation should be resumed from a
# previously saved state (if true) or start from scratch (if false). If auto
# is selected, models will be resumed if there is an existing checkpoint file,
# otherwise started from scratch.
set Resume computation                         = false

# The start time of the simulation. Units: Years if the 'Use years in output
# instead of seconds' parameter is set; seconds otherwise.
set Start time                                 = 0.

# The value the pressure is normalized to in each time step when `Pressure
# normalization' is set to `surface' with default value 0. This setting is
# ignored in all other cases.
# 
# The mathematical equations that describe thermal convection only determine
# the pressure up to an arbitrary constant. On the other hand, for comparison
# and for looking up material parameters it is important that the pressure be
# normalized somehow. We do this by enforcing a particular average pressure
# value at the surface of the domain, where the geometry model determines
# where the surface is. This parameter describes what this average surface
# pressure value is supposed to be. By default, it is set to zero, but one may
# want to choose a different value for example for simulating only the volume
# of the mantle below the lithosphere, in which case the surface pressure
# should be the lithostatic pressure at the bottom of the lithosphere.
# 
# For more information, see the section in the manual that discusses the
# general mathematical model.
set Surface pressure                           = 0                                                                                                               # default: 0.

# How frequently in timesteps to output timing information. This is generally
# adjusted only for debugging and timing purposes. If the value is set to zero
# it will also output timing information at the initiation timesteps.
set Timing output frequency                    = 100

# Mantle convection simulations are often focused on convection dominated
# systems. However, these codes can also be used to investigate systems where
# heat conduction plays a dominant role. This parameter indicates whether the
# simulator should also use heat conduction in determining the length of each
# time step.
set Use conduction timestep                    = true                                                                                                            # default: false

# If set to true, the advection and reactions of compositional fields and
# temperature are solved separately, and can use different time steps. Note
# that this will only work if the material/heating model fills the
# reaction\_rates/heating\_reaction\_rates structures. Operator splitting can
# be used with any existing solver schemes that solve the
# temperature/composition equations.
set Use operator splitting                     = false

# When computing results for mantle convection simulations, it is often
# difficult to judge the order of magnitude of results when they are stated in
# MKS units involving seconds. Rather, some kinds of results such as
# velocities are often stated in terms of meters per year (or, sometimes,
# centimeters per year). On the other hand, for non-dimensional computations,
# one wants results in their natural unit system as used inside the code. If
# this flag is set to `true' conversion to years happens; if it is `false', no
# such conversion happens.
# 
# Contrary to the word ``output'' in the name of this parameter, a number of
# plugins also use this parameter to determine how to interpret their
# \textit{inputs}. For example, when `true', several of the boundary velocity
# models described in Section~\ref{parameters:Boundary_20velocity_20model}
# interpret both specific times in years instead of seconds, and velocities in
# meters per year instead of meters per second.
set Use years in output instead of seconds     = true

# Name of the world builder file. If empty, the world builder is not
# initialized.
set World builder file                         = 


subsection Adiabatic conditions model
  # Select one of the following models:
  # 
  # `ascii data': A model in which the adiabatic profile is read from a file
  # that describes the reference state. Note the required format of the input
  # data: The first lines may contain any number of comments if they begin
  # with `#', but one of these lines needs to contain the number of points in
  # the reference state as for example `# POINTS: 3'. Following the comment
  # lines there has to be a single line containing the names of all data
  # columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide columns named `temperature',
  # `pressure', and `density'. Note that the data lines in the file need to be
  # sorted in order of increasing depth from 0 to the maximal depth in the
  # model domain. Points in the model that are outside of the provided depth
  # range will be assigned the maximum or minimum depth values, respectively.
  # Points do not need to be equidistant, but the computation of properties is
  # optimized in speed if they are.
  # 
  # `compute profile': A model in which the adiabatic profile is calculated by
  # solving the hydrostatic equations for pressure and temperature in depth.
  # The gravity is assumed to be in depth direction and the composition is
  # either given by the initial composition at reference points or computed as
  # a reference depth-function. All material parameters are computed by the
  # material model plugin. The surface conditions are either constant or
  # changing over time as prescribed by a user-provided function.
  # 
  # `function': A model in which the adiabatic profile is specified by a user
  # defined function. The supplied function has to contain temperature,
  # pressure, and density as a function of depth in this order.
  set Model name = compute profile


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory = $ASPECT_SOURCE_DIR/tests/adiabatic-conditions/ascii-data/test/

    # The file name of the model data.
    set Data file name = 

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor   = 1.
  end

  subsection Compute profile
    # Select how the reference profile for composition is computed. This
    # profile is used to evaluate the material model, when computing the
    # pressure and temperature profile.
    set Composition reference profile  = initial composition

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants             = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression            = 0

    # The number of points we use to compute the adiabatic profile. The higher
    # the number of points, the more accurate the downward integration from
    # the adiabatic surface temperature will be.
    set Number of points               = 1000

    # Whether to use the 'Surface condition function' to determine surface
    # conditions, or the 'Adiabatic surface temperature' and 'Surface
    # pressure' parameters. If this is set to true the reference profile is
    # updated every timestep. The function expression of the function should
    # be independent of space, but can depend on time 't'. The function must
    # return two components, the first one being reference surface pressure,
    # the second one being reference surface temperature.
    set Use surface condition function = false

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names                 = x,t


    subsection Surface condition function
      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants  = 

      # The formula that denotes the function you want to evaluate for
      # particular values of the independent variables. This expression may
      # contain any of the usual operations such as addition or
      # multiplication, as well as all of the common functions such as `sin'
      # or `cos'. In addition, it may contain expressions like `if(x>0, 1,
      # -1)' where the expression evaluates to the second argument if the
      # first argument is true, and to the third argument otherwise. For a
      # full overview of possible expressions accepted see the documentation
      # of the muparser library at http://muparser.beltoforion.de/.
      # 
      # If the function you are describing represents a vector-valued function
      # with multiple components, then separate the expressions for individual
      # components by a semicolon.
      set Function expression = 0; 0

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names      = x,t
    end

  end

  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # Expression for the adiabatic temperature, pressure, and density
    # separated by semicolons as a function of `depth'.
    set Function expression = 0.0; 0.0; 1.0
    set Variable names      = depth
  end

end


subsection Boundary composition model
  # When the composition is fixed on a given boundary as determined by the
  # list of 'Fixed composition boundary indicators', there might be parts of
  # the boundary where material flows out and one may want to prescribe the
  # composition only on those parts of the boundary where there is inflow.
  # This parameter determines if compositions are only prescribed at these
  # inflow parts of the boundary (if false) or everywhere on a given boundary,
  # independent of the flow direction (if true). By default, this parameter is
  # set to false, except in models with melt transport (see below). Note that
  # in this context, `fixed' refers to the fact that these are the boundary
  # indicators where Dirichlet boundary conditions are applied, and does not
  # imply that the boundary composition is time-independent.
  # 
  # Mathematically speaking, the compositional fields satisfy an advection
  # equation that has no diffusion. For this equation, one can only impose
  # Dirichlet boundary conditions (i.e., prescribe a fixed compositional field
  # value at the boundary) at those boundaries where material flows in. This
  # would correspond to the ``false'' setting of this parameter, which is
  # correspondingly the default. On the other hand, on a finite dimensional
  # discretization such as the one one obtains from the finite element method,
  # it is possible to also prescribe values on outflow boundaries, even though
  # this may make no physical sense. This would then correspond to the
  # ``true'' setting of this parameter.
  # 
  # A warning for models with melt transport: In models with fluid flow, some
  # compositional fields (in particular the porosity) might be transported
  # with the fluid velocity, and would need to set the constraints based on
  # the fluid velocity. However, this is currently not possible, because we
  # reuse the same matrix for all compositional fields, and therefore can not
  # use different constraints for different fields. Consequently, we set this
  # parameter to true by default in models where melt transport is enabled. Be
  # aware that if you change this default setting, you will not use the melt
  # velocity, but the solid velocity to determine on which parts of the
  # boundaries there is outflow.
  set Allow fixed composition on outflow boundaries = false for models without melt

  # A comma separated list of names denoting those boundaries on which the
  # composition is fixed and described by the boundary composition object
  # selected in its own section of this input file. All boundary indicators
  # used by the geometry but not explicitly listed here will end up with
  # no-flux (insulating) boundary conditions.
  # 
  # The names of the boundaries listed here can either be numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  # 
  # This parameter only describes which boundaries have a fixed composition,
  # but not what composition should hold on these boundaries. The latter piece
  # of information needs to be implemented in a plugin in the
  # BoundaryComposition group, unless an existing implementation in this group
  # already provides what you want.
  set Fixed composition boundary indicators         = 

  # A comma-separated list of boundary composition models that will be used to
  # initialize the composition. These plugins are loaded in the order given,
  # and modify the existing composition field via the operators listed in
  # 'List of model operators'.
  # 
  # The following boundary composition models are available:
  # 
  # `ascii data': Implementation of a model in which the boundary composition
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `composition1',
  # `composition2', etc. in a 2d model and `x', `y', `composition1',
  # `composition2', etc., in a 3d model, according to the number of
  # compositional fields, which means that there has to be a single column for
  # every composition in the model. Note that the data in the input files need
  # to be sorted in a specific order: the first coordinate needs to ascend
  # first, followed by the second in order to assign the correct data to the
  # prescribed coordinates.If you use a spherical model, then the assumed grid
  # changes. `x' will be replaced by the radial distance of the point to the
  # bottom of the model, `y' by the azimuth angle and `z' by the polar angle
  # measured positive from the north pole. The grid will be assumed to be a
  # latitude-longitude grid. Note that the order of spherical coordinates is
  # `r', `phi', `theta' and not `r', `theta', `phi', since this allows for
  # dimension independent expressions.
  # 
  # `box': A model in which the composition is chosen constant on the sides of
  # a box which are selected by the parameters
  # Left/Right/Top/Bottom/Front/Back composition
  # 
  # `box with lithosphere boundary indicators': A model in which the
  # composition is chosen constant on all the sides of a box. Additional
  # boundary indicators are added to the lithospheric parts of the vertical
  # boundaries. This model is to be used with the 'Two Merged Boxes' Geometry
  # Model.
  # 
  # `function': Implementation of a model in which the boundary composition is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary composition model|Function''.
  # 
  # Since the symbol $t$ indicating time may appear in the formulas for the
  # prescribed composition, it is interpreted as having units seconds unless
  # the global input parameter ``Use years in output instead of seconds'' is
  # set, in which case we interpret the formula expressions as having units
  # year.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `initial composition': A model in which the composition at the boundary is
  # chosen to be the same as given in the initial conditions.
  # 
  # Because this class simply takes what the initial composition had
  # described, this class can not know certain pieces of information such as
  # the minimal and maximal composition on the boundary. For operations that
  # require this, for example in post-processing, this boundary composition
  # model must therefore be told what the minimal and maximal values on the
  # boundary are. This is done using parameters set in section ``Boundary
  # composition model/Initial composition''.
  # 
  # `spherical constant': A model in which the composition is chosen constant
  # on the inner and outer boundaries of a surface, spherical shell, chunk or
  # ellipsoidal chunk. Parameters are read from subsection 'Spherical
  # constant'.
  set List of model names                           = 

  # A comma-separated list of operators that will be used to append the listed
  # composition models onto the previous models. If only one operator is
  # given, the same operator is applied to all models.
  set List of model operators                       = add

  # Select one of the following models:
  # 
  # `ascii data': Implementation of a model in which the boundary composition
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `composition1',
  # `composition2', etc. in a 2d model and `x', `y', `composition1',
  # `composition2', etc., in a 3d model, according to the number of
  # compositional fields, which means that there has to be a single column for
  # every composition in the model. Note that the data in the input files need
  # to be sorted in a specific order: the first coordinate needs to ascend
  # first, followed by the second in order to assign the correct data to the
  # prescribed coordinates.If you use a spherical model, then the assumed grid
  # changes. `x' will be replaced by the radial distance of the point to the
  # bottom of the model, `y' by the azimuth angle and `z' by the polar angle
  # measured positive from the north pole. The grid will be assumed to be a
  # latitude-longitude grid. Note that the order of spherical coordinates is
  # `r', `phi', `theta' and not `r', `theta', `phi', since this allows for
  # dimension independent expressions.
  # 
  # `box': A model in which the composition is chosen constant on the sides of
  # a box which are selected by the parameters
  # Left/Right/Top/Bottom/Front/Back composition
  # 
  # `box with lithosphere boundary indicators': A model in which the
  # composition is chosen constant on all the sides of a box. Additional
  # boundary indicators are added to the lithospheric parts of the vertical
  # boundaries. This model is to be used with the 'Two Merged Boxes' Geometry
  # Model.
  # 
  # `function': Implementation of a model in which the boundary composition is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary composition model|Function''.
  # 
  # Since the symbol $t$ indicating time may appear in the formulas for the
  # prescribed composition, it is interpreted as having units seconds unless
  # the global input parameter ``Use years in output instead of seconds'' is
  # set, in which case we interpret the formula expressions as having units
  # year.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `initial composition': A model in which the composition at the boundary is
  # chosen to be the same as given in the initial conditions.
  # 
  # Because this class simply takes what the initial composition had
  # described, this class can not know certain pieces of information such as
  # the minimal and maximal composition on the boundary. For operations that
  # require this, for example in post-processing, this boundary composition
  # model must therefore be told what the minimal and maximal values on the
  # boundary are. This is done using parameters set in section ``Boundary
  # composition model/Initial composition''.
  # 
  # `spherical constant': A model in which the composition is chosen constant
  # on the inner and outer boundaries of a surface, spherical shell, chunk or
  # ellipsoidal chunk. Parameters are read from subsection 'Spherical
  # constant'.
  # 
  # \textbf{Warning}: This parameter provides an old and deprecated way of
  # specifying boundary composition models and shouldn't be used. Please use
  # 'List of model names' instead.
  set Model name                                    = unspecified


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-composition/ascii-data/test/

    # The file name of the model data. Provide file in format: (File
    # name).\%s\%d, where \%s is a string specifying the boundary of the model
    # according to the names of the boundary indicators (of the chosen
    # geometry model), and \%d is any sprintf integer qualifier specifying the
    # format of the current file number.
    set Data file name             = box_2d_%s.%d.txt

    # Time step between following data files. Depending on the setting of the
    # global `Use years in output instead of seconds' flag in the input file,
    # this number is either interpreted as seconds or as years. The default is
    # one million, i.e., either one million seconds or one million years.
    set Data file time step        = 1e6

    # In some cases the boundary files are not numbered in increasing but in
    # decreasing order (e.g. `Ma BP'). If this flag is set to `True' the
    # plugin will first load the file with the number `First data file number'
    # and decrease the file number during the model run.
    set Decreasing file order      = false

    # Time from which on the data file with number `First data file number' is
    # used as boundary condition. Until this time, a boundary condition equal
    # to zero everywhere is assumed. Depending on the setting of the global
    # `Use years in output instead of seconds' flag in the input file, this
    # number is either interpreted as seconds or as years.
    set First data file model time = 0

    # Number of the first velocity file to be loaded when the model time is
    # larger than `First velocity file model time'.
    set First data file number     = 0

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor               = 1.
  end

  subsection Box
    # A comma separated list of composition boundary values at the bottom
    # boundary (at minimal $y$-value in 2d, or minimal $z$-value in 3d). This
    # list must have as many entries as there are compositional fields. Units:
    # none.
    set Bottom composition = 

    # A comma separated list of composition boundary values at the left
    # boundary (at minimal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Left composition   = 

    # A comma separated list of composition boundary values at the right
    # boundary (at maximal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Right composition  = 

    # A comma separated list of composition boundary values at the top
    # boundary (at maximal $y$-value in 2d, or maximal $z$-value in 3d). This
    # list must have as many entries as there are compositional fields. Units:
    # none.
    set Top composition    = 
  end

  subsection Box with lithosphere boundary indicators
    # A comma separated list of composition boundary values at the bottom
    # boundary (at minimal $y$-value in 2d, or minimal $z$-value in 3d). This
    # list must have as many entries as there are compositional fields. Units:
    # none.
    set Bottom composition            = 

    # A comma separated list of composition boundary values at the left
    # boundary (at minimal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Left composition              = 

    # A comma separated list of composition boundary values at the left
    # boundary (at minimal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Left composition lithosphere  = 

    # A comma separated list of composition boundary values at the right
    # boundary (at maximal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Right composition             = 

    # A comma separated list of composition boundary values at the right
    # boundary (at maximal $x$-value). This list must have as many entries as
    # there are compositional fields. Units: none.
    set Right composition lithosphere = 

    # A comma separated list of composition boundary values at the top
    # boundary (at maximal $y$-value in 2d, or maximal $z$-value in 3d). This
    # list must have as many entries as there are compositional fields. Units:
    # none.
    set Top composition               = 
  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are 'cartesian', 'spherical', and
    # 'depth'. 'spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. 'depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Initial composition
    # Maximal composition. Units: none.
    set Maximal composition = 1.

    # Minimal composition. Units: none.
    set Minimal composition = 0.
  end

  subsection Spherical constant
    # Composition at the inner boundary (core mantle boundary). Units: none.
    set Inner composition = 1.

    # Composition at the outer boundary (lithosphere water/air). For a
    # spherical geometry model, this is the only boundary. Units: none.
    set Outer composition = 0.
  end

end


subsection Boundary fluid pressure model
  # Select one of the following plugins:
  # 
  # `density': A plugin that prescribes the fluid pressure gradient at the
  # boundary based on fluid/solid density from the material model.
  set Plugin name = density


  subsection Density
    # The density formulation used to compute the fluid pressure gradient at
    # the model boundary.
    # 
    # `solid density' prescribes the gradient of the fluid pressure as solid
    # density times gravity (which is the lithostatic pressure) and leads to
    # approximately the same pressure in the melt as in the solid, so that
    # fluid is only flowing in or out due to differences in dynamic pressure.
    # 
    # `fluid density' prescribes the gradient of the fluid pressure as fluid
    # density times gravity and causes melt to flow in with the same velocity
    # as inflowing solid material, or no melt flowing in or out if the solid
    # velocity normal to the boundary is zero.
    # 
    # 'average density' prescribes the gradient of the fluid pressure as the
    # averaged fluid and solid density times gravity (which is a better
    # approximation for the lithostatic pressure than just the solid density)
    # and leads to approximately the same pressure in the melt as in the
    # solid, so that fluid is only flowing in or out due to differences in
    # dynamic pressure.
    set Density formulation = solid density
  end

end


subsection Boundary heat flux model
  # A comma separated list of names denoting those boundaries on which the
  # heat flux is fixed and described by the boundary heat flux object selected
  # in the 'Model name' parameter. All boundary indicators used by the
  # geometry but not explicitly listed here or in the list of 'Fixed
  # temperature boundary indicators' in the 'Boundary temperature model' will
  # end up with no-flux (insulating) boundary conditions.
  # 
  # The names of the boundaries listed here can either be numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  # 
  # This parameter only describes which boundaries have a fixed heat flux, but
  # not what heat flux should hold on these boundaries. The latter piece of
  # information needs to be implemented in a plugin in the BoundaryHeatFlux
  # group, unless an existing implementation in this group already provides
  # what you want.
  set Fixed heat flux boundary indicators = 

  # Select one of the following plugins:
  # 
  # `function': Implementation of a model in which the boundary heat flux is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary heat flux model|Function''. The format of these
  # functions follows the syntax understood by the muparser library, see
  # Section~\ref{sec:muparser-format}.
  # 
  # The formula you describe in the mentioned section is a scalar value for
  # the heat flux that is assumed to be the flux normal to the boundary, and
  # that has the unit W/(m$^2$) (in 3d) or W/m (in 2d). Negative fluxes are
  # interpreted as the flow of heat into the domain, and positive fluxes are
  # interpreted as heat flowing out of the domain.
  # 
  # The symbol $t$ indicating time that may appear in the formulas for the
  # prescribed heat flux is interpreted as having units seconds unless the
  # global parameter ``Use years in output instead of seconds'' has been set.
  set Model name                          = function


  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

end


subsection Boundary temperature model
  # When the temperature is fixed on a given boundary as determined by the
  # list of 'Fixed temperature boundary indicators', there might be parts of
  # the boundary where material flows out and one may want to prescribe the
  # temperature only on the parts of the boundary where there is inflow. This
  # parameter determines if temperatures are only prescribed at these inflow
  # parts of the boundary (if false) or everywhere on a given boundary,
  # independent of the flow direction (if true).Note that in this context,
  # `fixed' refers to the fact that these are the boundary indicators where
  # Dirichlet boundary conditions are applied, and does not imply that the
  # boundary temperature is time-independent.
  # 
  # Mathematically speaking, the temperature satisfies an advection-diffusion
  # equation. For this type of equation, one can prescribe the temperature
  # even on outflow boundaries as long as the diffusion coefficient is
  # nonzero. This would correspond to the ``true'' setting of this parameter,
  # which is correspondingly the default. In practice, however, this would
  # only make physical sense if the diffusion coefficient is actually quite
  # large to prevent the creation of a boundary layer. In addition, if there
  # is no diffusion, one can only impose Dirichlet boundary conditions (i.e.,
  # prescribe a fixed temperature value at the boundary) at those boundaries
  # where material flows in. This would correspond to the ``false'' setting of
  # this parameter.
  set Allow fixed temperature on outflow boundaries = true

  # A comma separated list of names denoting those boundaries on which the
  # temperature is fixed and described by the boundary temperature object
  # selected in the 'List of model names' parameter. All boundary indicators
  # used by the geometry but not explicitly listed here will end up with
  # no-flux (insulating) boundary conditions, or, if they are listed in the
  # 'Fixed heat flux boundary indicators', with Neumann boundary conditions.
  # 
  # The names of the boundaries listed here can either be numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  # 
  # This parameter only describes which boundaries have a fixed temperature,
  # but not what temperature should hold on these boundaries. The latter piece
  # of information needs to be implemented in a plugin in the
  # BoundaryTemperature group, unless an existing implementation in this group
  # already provides what you want.
  set Fixed temperature boundary indicators         = top, left, right    # default: 

  # A comma-separated list of boundary temperature models that will be used to
  # initialize the temperature. These plugins are loaded in the order given,
  # and modify the existing temperature field via the operators listed in
  # 'List of model operators'.
  # 
  # The following boundary temperature models are available:
  # 
  # `ascii data': Implementation of a model in which the boundary data is
  # derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `Temperature [K]' in a 2d
  # model and  `x', `y', `Temperature [K]' in a 3d model, which means that
  # there has to be a single column containing the temperature. Note that the
  # data in the input files need to be sorted in a specific order: the first
  # coordinate needs to ascend first, followed by the second in order to
  # assign the correct data to the prescribed coordinates. If you use a
  # spherical model, then the assumed grid changes. `x' will be replaced by
  # the radial distance of the point to the bottom of the model, `y' by the
  # azimuth angle and `z' by the polar angle measured positive from the north
  # pole. The grid will be assumed to be a latitude-longitude grid. Note that
  # the order of spherical coordinates is `r', `phi', `theta' and not `r',
  # `theta', `phi', since this allows for dimension independent expressions.
  # 
  # `box': A model in which the temperature is chosen constant on the sides of
  # a box which are selected by the parameters
  # Left/Right/Top/Bottom/Front/Back temperature
  # 
  # `box with lithosphere boundary indicators': A model in which the
  # temperature is chosen constant on all the sides of a box. Additional
  # boundary indicators are added to the lithospheric parts of the vertical
  # boundaries. This model is to be used with the 'Two Merged Boxes' Geometry
  # Model.
  # 
  # `constant': A model in which the temperature is chosen constant on a given
  # boundary indicator.  Parameters are read from the subsection 'Constant'.
  # 
  # `dynamic core': This is a boundary temperature model working only with
  # spherical shell geometry and core statistics postprocessor. The
  # temperature at the top is constant, and the core mantle boundary
  # temperature is dynamically evolving through time by calculating the heat
  # flux into the core and solving the core energy balance. The formulation is
  # mainly following \cite{NPB+04}, and the plugin is used in Zhang et al.
  # [2016]. The energy of core cooling and freeing of the inner core is
  # included in the plugin. However, current plugin can not deal with the
  # energy balance if the core is in the `snowing core' regime (i.e., the core
  # solidifies from the top instead of bottom).
  # 
  # `function': Implementation of a model in which the boundary temperature is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary temperature model|Function''.
  # 
  # Since the symbol $t$ indicating time may appear in the formulas for the
  # prescribed temperatures, it is interpreted as having units seconds unless
  # the global input parameter ``Use years in output instead of seconds'' is
  # set, in which case we interpret the formula expressions as having units
  # year.
  # 
  # Because this class simply takes what the function calculates, this class
  # can not know certain pieces of information such as the minimal and maximal
  # temperature on the boundary. For operations that require this, for example
  # in post-processing, this boundary temperature model must therefore be told
  # what the minimal and maximal values on the boundary are. This is done
  # using parameters set in section ``Boundary temperature model/Initial
  # temperature''.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `initial temperature': A model in which the temperature at the boundary is
  # chosen to be the same as given in the initial conditions.
  # 
  # Because this class simply takes what the initial temperature had
  # described, this class can not know certain pieces of information such as
  # the minimal and maximal temperature on the boundary. For operations that
  # require this, for example in post-processing, this boundary temperature
  # model must therefore be told what the minimal and maximal values on the
  # boundary are. This is done using parameters set in section ``Boundary
  # temperature model/Initial temperature''.
  # 
  # `spherical constant': A model in which the temperature is chosen constant
  # on the inner and outer boundaries of a spherical shell, ellipsoidal chunk
  # or chunk. Parameters are read from subsection 'Spherical constant'.
  set List of model names                           = initial temperature # default: 

  # A comma-separated list of operators that will be used to append the listed
  # temperature models onto the previous models. If only one operator is
  # given, the same operator is applied to all models.
  set List of model operators                       = add

  # Select one of the following models:
  # 
  # `ascii data': Implementation of a model in which the boundary data is
  # derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `Temperature [K]' in a 2d
  # model and  `x', `y', `Temperature [K]' in a 3d model, which means that
  # there has to be a single column containing the temperature. Note that the
  # data in the input files need to be sorted in a specific order: the first
  # coordinate needs to ascend first, followed by the second in order to
  # assign the correct data to the prescribed coordinates. If you use a
  # spherical model, then the assumed grid changes. `x' will be replaced by
  # the radial distance of the point to the bottom of the model, `y' by the
  # azimuth angle and `z' by the polar angle measured positive from the north
  # pole. The grid will be assumed to be a latitude-longitude grid. Note that
  # the order of spherical coordinates is `r', `phi', `theta' and not `r',
  # `theta', `phi', since this allows for dimension independent expressions.
  # 
  # `box': A model in which the temperature is chosen constant on the sides of
  # a box which are selected by the parameters
  # Left/Right/Top/Bottom/Front/Back temperature
  # 
  # `box with lithosphere boundary indicators': A model in which the
  # temperature is chosen constant on all the sides of a box. Additional
  # boundary indicators are added to the lithospheric parts of the vertical
  # boundaries. This model is to be used with the 'Two Merged Boxes' Geometry
  # Model.
  # 
  # `constant': A model in which the temperature is chosen constant on a given
  # boundary indicator.  Parameters are read from the subsection 'Constant'.
  # 
  # `dynamic core': This is a boundary temperature model working only with
  # spherical shell geometry and core statistics postprocessor. The
  # temperature at the top is constant, and the core mantle boundary
  # temperature is dynamically evolving through time by calculating the heat
  # flux into the core and solving the core energy balance. The formulation is
  # mainly following \cite{NPB+04}, and the plugin is used in Zhang et al.
  # [2016]. The energy of core cooling and freeing of the inner core is
  # included in the plugin. However, current plugin can not deal with the
  # energy balance if the core is in the `snowing core' regime (i.e., the core
  # solidifies from the top instead of bottom).
  # 
  # `function': Implementation of a model in which the boundary temperature is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary temperature model|Function''.
  # 
  # Since the symbol $t$ indicating time may appear in the formulas for the
  # prescribed temperatures, it is interpreted as having units seconds unless
  # the global input parameter ``Use years in output instead of seconds'' is
  # set, in which case we interpret the formula expressions as having units
  # year.
  # 
  # Because this class simply takes what the function calculates, this class
  # can not know certain pieces of information such as the minimal and maximal
  # temperature on the boundary. For operations that require this, for example
  # in post-processing, this boundary temperature model must therefore be told
  # what the minimal and maximal values on the boundary are. This is done
  # using parameters set in section ``Boundary temperature model/Initial
  # temperature''.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `initial temperature': A model in which the temperature at the boundary is
  # chosen to be the same as given in the initial conditions.
  # 
  # Because this class simply takes what the initial temperature had
  # described, this class can not know certain pieces of information such as
  # the minimal and maximal temperature on the boundary. For operations that
  # require this, for example in post-processing, this boundary temperature
  # model must therefore be told what the minimal and maximal values on the
  # boundary are. This is done using parameters set in section ``Boundary
  # temperature model/Initial temperature''.
  # 
  # `spherical constant': A model in which the temperature is chosen constant
  # on the inner and outer boundaries of a spherical shell, ellipsoidal chunk
  # or chunk. Parameters are read from subsection 'Spherical constant'.
  # 
  # \textbf{Warning}: This parameter provides an old and deprecated way of
  # specifying boundary temperature models and shouldn't be used. Please use
  # 'List of model names' instead.
  set Model name                                    = unspecified


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-temperature/ascii-data/test/

    # The file name of the model data. Provide file in format: (File
    # name).\%s\%d, where \%s is a string specifying the boundary of the model
    # according to the names of the boundary indicators (of the chosen
    # geometry model), and \%d is any sprintf integer qualifier specifying the
    # format of the current file number.
    set Data file name             = box_2d_%s.%d.txt

    # Time step between following data files. Depending on the setting of the
    # global `Use years in output instead of seconds' flag in the input file,
    # this number is either interpreted as seconds or as years. The default is
    # one million, i.e., either one million seconds or one million years.
    set Data file time step        = 1e6

    # In some cases the boundary files are not numbered in increasing but in
    # decreasing order (e.g. `Ma BP'). If this flag is set to `True' the
    # plugin will first load the file with the number `First data file number'
    # and decrease the file number during the model run.
    set Decreasing file order      = false

    # Time from which on the data file with number `First data file number' is
    # used as boundary condition. Until this time, a boundary condition equal
    # to zero everywhere is assumed. Depending on the setting of the global
    # `Use years in output instead of seconds' flag in the input file, this
    # number is either interpreted as seconds or as years.
    set First data file model time = 0

    # Number of the first velocity file to be loaded when the model time is
    # larger than `First velocity file model time'.
    set First data file number     = 0

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor               = 1.
  end

  subsection Box
    # Temperature at the bottom boundary (at minimal $z$-value). Units:
    # \si{\kelvin}.
    set Bottom temperature = 0.

    # Temperature at the left boundary (at minimal $x$-value). Units:
    # \si{\kelvin}.
    set Left temperature   = 1.

    # Temperature at the right boundary (at maximal $x$-value). Units:
    # \si{\kelvin}.
    set Right temperature  = 0.

    # Temperature at the top boundary (at maximal $x$-value). Units:
    # \si{\kelvin}.
    set Top temperature    = 0.
  end

  subsection Box with lithosphere boundary indicators
    # Temperature at the bottom boundary (at minimal $z$-value). Units:
    # \si{\kelvin}.
    set Bottom temperature            = 0.

    # Temperature at the left boundary (at minimal $x$-value). Units:
    # \si{\kelvin}.
    set Left temperature              = 1.

    # Temperature at the additional left lithosphere boundary (specified by
    # user in Geometry Model). Units: \si{\kelvin}.
    set Left temperature lithosphere  = 0.

    # Temperature at the right boundary (at maximal $x$-value). Units:
    # \si{\kelvin}.
    set Right temperature             = 0.

    # Temperature at the additional right lithosphere boundary (specified by
    # user in Geometry Model). Units: \si{\kelvin}.
    set Right temperature lithosphere = 0.

    # Temperature at the top boundary (at maximal $x$-value). Units:
    # \si{\kelvin}.
    set Top temperature               = 0.
  end

  subsection Constant
    # A comma separated list of mappings between boundary indicators and the
    # temperature associated with the boundary indicators. The format for this
    # list is ``indicator1 : value1, indicator2 : value2, ...'', where each
    # indicator is a valid boundary indicator (either a number or the symbolic
    # name of a boundary as provided by the geometry model) and each value is
    # the temperature of that boundary.
    set Boundary indicator to temperature mappings = 
  end

  subsection Dynamic core
    # Core thermal expansivity. Units: \si{\per\kelvin}.
    set Alpha                     = 1.35e-5

    # Compositional expansion coefficient $Beta_c$. See \cite{NPB+04} for more
    # details.
    set Beta composition          = 1.1

    # Pressure at CMB. Units: \si{\pascal}.
    set CMB pressure              = 0.14e12

    # Core heat conductivity $k_c$. Units: \si{\watt\per\meter\per\kelvin}.
    set Core conductivity         = 60.

    # Density of the core. Units: \si{\kilogram\per\meter\cubed}.
    set Core density              = 12.5e3

    # Heat capacity of the core. Units: \si{\joule\per\kelvin\per\kilogram}.
    set Core heat capacity        = 840.

    # Partition coefficient of the light element.
    set Delta                     = 0.5

    # Gravitation acceleration at CMB. Units: \si{\meter\per\second\squared}.
    set Gravity acceleration      = 9.8

    # Initial light composition (eg. S,O) concentration in weight fraction.
    set Initial light composition = 0.01

    # Temperature at the inner boundary (core mantle boundary) at the
    # beginning. Units: \si{\kelvin}.
    set Inner temperature         = 6000.

    # Core compressibility at zero pressure. See \cite{NPB+04} for more
    # details.
    set K0                        = 4.111e11

    # The latent heat of core freeze. Units: \si{\joule\per\kilogram}.
    set Lh                        = 750e3

    # The max iterations for nonlinear core energy solver.
    set Max iteration             = 30000

    # Temperature at the outer boundary (lithosphere water/air). Units:
    # \si{\kelvin}.
    set Outer temperature         = 0.

    # The heat of reaction. Units: \si{\joule\per\kilogram}.
    set Rh                        = -27.7e6

    # Core density at zero pressure. Units: \si{\kilogram\per\meter\cubed}.
    # See \cite{NPB+04} for more details.
    set Rho0                      = 7.019e3

    # Initial inner core radius changing rate. Units: \si{\kilo\meter}/year.
    set dR over dt                = 0.

    # Initial CMB temperature changing rate. Units: \si{\kelvin}/year.
    set dT over dt                = 0.

    # Initial light composition changing rate. Units: 1/year.
    set dX over dt                = 0.


    subsection Geotherm parameters
      # If melting curve dependent on composition.
      set Composition dependency = true

      # Melting curve (\cite{NPB+04} eq. (40)) parameter Theta.
      set Theta                  = 0.11

      # Melting curve (\cite{NPB+04} eq. (40)) parameter Tm0. Units:
      # \si{\kelvin}.
      set Tm0                    = 1695.

      # Melting curve (\cite{NPB+04} eq. (40)) parameter Tm1. Units:
      # \si{\per\tera\pascal}.
      set Tm1                    = 10.9

      # Melting curve (\cite{NPB+04} eq. (40)) parameter Tm2. Units:
      # \si{\per\tera\pascal\squared}.
      set Tm2                    = -8.0

      # If using the Fe-FeS system solidus from Buono \& Walker (2011)
      # instead.
      set Use BW11               = false
    end

    subsection Other energy source
      # Data file name for other energy source into the core. The 'other
      # energy source' is used for external core energy source.For example if
      # someone want to test the early lunar core powered by precession
      # (Dwyer, C. A., et al. (2011). A long-lived lunar dynamo driven by
      # continuous mechanical stirring. Nature 479(7372): 212-214.)Format
      # [Time(Gyr)   Energy rate(W)]
      set File name = 
    end

    subsection Radioactive heat source
      # Half decay times of different elements (Ga)
      set Half life times                        = 

      # Heating rates of different elements (W/kg)
      set Heating rates                          = 

      # Initial concentrations of different elements (ppm)
      set Initial concentrations                 = 

      # Number of different radioactive heating elements in core
      set Number of radioactive heating elements = 0
    end

  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # Maximal temperature. Units: \si{\kelvin}.
    set Maximal temperature = 3773.

    # Minimal temperature. Units: \si{\kelvin}.
    set Minimal temperature = 273.

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Initial temperature
    # Maximal temperature. Units: \si{\kelvin}.
    set Maximal temperature = 3773.

    # Minimal temperature. Units: \si{\kelvin}.
    set Minimal temperature = 0.
  end

  subsection Spherical constant
    # Temperature at the inner boundary (core mantle boundary). Units:
    # \si{\kelvin}.
    set Inner temperature = 6000.

    # Temperature at the outer boundary (lithosphere water/air). Units:
    # \si{\kelvin}.
    set Outer temperature = 0.
  end

end


subsection Boundary traction model
  # A comma separated list denoting those boundaries on which a traction force
  # is prescribed, i.e., where known external forces act, resulting in an
  # unknown velocity. This is often used to model ``open'' boundaries where we
  # only know the pressure. This pressure then produces a force that is normal
  # to the boundary and proportional to the pressure.
  # 
  # The format of valid entries for this parameter is that of a map given as
  # ``key1 [selector]: value1, key2 [selector]: value2, key3: value3, ...''
  # where each key must be a valid boundary indicator (which is either an
  # integer or the symbolic name the geometry model in use may have provided
  # for this part of the boundary) and each value must be one of the currently
  # implemented boundary traction models. ``selector'' is an optional string
  # given as a subset of the letters `xyz' that allows you to apply the
  # boundary conditions only to the components listed. As an example, '1 y:
  # function' applies the type `function' to the y component on boundary 1.
  # Without a selector it will affect all components of the traction.
  set Prescribed traction boundary indicators = right: zero traction, bottom:zero traction # default: 


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-traction/ascii-data/test/

    # The file name of the model data. Provide file in format: (File
    # name).\%s\%d, where \%s is a string specifying the boundary of the model
    # according to the names of the boundary indicators (of the chosen
    # geometry model), and \%d is any sprintf integer qualifier specifying the
    # format of the current file number.
    set Data file name             = box_2d_%s.%d.txt

    # Time step between following data files. Depending on the setting of the
    # global `Use years in output instead of seconds' flag in the input file,
    # this number is either interpreted as seconds or as years. The default is
    # one million, i.e., either one million seconds or one million years.
    set Data file time step        = 1e6

    # In some cases the boundary files are not numbered in increasing but in
    # decreasing order (e.g. `Ma BP'). If this flag is set to `True' the
    # plugin will first load the file with the number `First data file number'
    # and decrease the file number during the model run.
    set Decreasing file order      = false

    # Time from which on the data file with number `First data file number' is
    # used as boundary condition. Until this time, a boundary condition equal
    # to zero everywhere is assumed. Depending on the setting of the global
    # `Use years in output instead of seconds' flag in the input file, this
    # number is either interpreted as seconds or as years.
    set First data file model time = 0

    # Number of the first velocity file to be loaded when the model time is
    # larger than `First velocity file model time'.
    set First data file number     = 0

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor               = 1.
  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Initial lithostatic pressure
    # The number of integration points over which we integrate the lithostatic
    # pressure downwards.
    set Number of integration points = 1000

    # The point where the pressure profile will be calculated. Cartesian
    # coordinates $(x,y,z)$ when geometry is a box, otherwise enter radius,
    # longitude, and in 3D latitude. Note that the coordinate related to the
    # depth ($y$ in 2D cartesian, $z$ in 3D cartesian and radius in spherical
    # coordinates) is not used. Units: \si{\meter} or degrees.
    set Representative point         = 
  end

end


subsection Boundary velocity model
  # A comma separated list denoting those boundaries on which the velocity is
  # prescribed, i.e., where unknown external forces act to prescribe a
  # particular velocity. This is often used to prescribe a velocity that
  # equals that of overlying plates.
  # 
  # The format of valid entries for this parameter is that of a map given as
  # ``key1 [selector]: value1, key2 [selector]: value2, key3: value3, ...''
  # where each key must be a valid boundary indicator (which is either an
  # integer or the symbolic name the geometry model in use may have provided
  # for this part of the boundary) and each value must be one of the currently
  # implemented boundary velocity models. ``selector'' is an optional string
  # given as a subset of the letters `xyz' that allows you to apply the
  # boundary conditions only to the components listed. As an example, '1 y:
  # function' applies the type `function' to the y component on boundary 1.
  # Without a selector it will affect all components of the velocity.
  # 
  # Note that the no-slip boundary condition is a special case of the current
  # one where the prescribed velocity happens to be zero. It can thus be
  # implemented by indicating that a particular boundary is part of the ones
  # selected using the current parameter and using ``zero velocity'' as the
  # boundary values. Alternatively, you can simply list the part of the
  # boundary on which the velocity is to be zero with the parameter ``Zero
  # velocity boundary indicator'' in the current parameter section.
  # 
  # Note that when ``Use years in output instead of seconds'' is set to true,
  # velocity should be given in m/yr. The following boundary velocity models
  # are available:
  # 
  # `ascii data': Implementation of a model in which the boundary velocity is
  # derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `velocity${}_x$',
  # `velocity${}_y$' in a 2d model or `x', `y', `velocity${}_x$',
  # `velocity${}_y$', `velocity${}_z$' in a 3d model. Note that the data in
  # the input files need to be sorted in a specific order: the first
  # coordinate needs to ascend first, followed by the second in order to
  # assign the correct data to the prescribed coordinates.If you use a
  # spherical model, then the assumed grid changes. `x' will be replaced by
  # the radial distance of the point to the bottom of the model, `y' by the
  # azimuth angle and `z' by the polar angle measured positive from the north
  # pole. The grid will be assumed to be a latitude-longitude grid. Note that
  # the order of spherical coordinates is `r', `phi', `theta' and not `r',
  # `theta', `phi', since this allows for dimension independent expressions.
  # Velocities can be specified using cartesian (by default) or spherical unit
  # vectors. No matter which geometry model is chosen, the unit of the
  # velocities is assumed to be m/s or m/yr depending on the `Use years in
  # output instead of seconds' flag. If you provide velocities in cm/yr, set
  # the `Scale factor' option to 0.01.
  # 
  # `function': Implementation of a model in which the boundary velocity is
  # given in terms of an explicit formula that is elaborated in the parameters
  # in section ``Boundary velocity model|Function''. The format of these
  # functions follows the syntax understood by the muparser library, see
  # Section~\ref{sec:muparser-format}.
  # 
  # The formula you describe in the mentioned section is a semicolon separated
  # list of velocities for each of the $d$ components of the velocity vector.
  # These $d$ formulas are interpreted as having units m/s, unless the global
  # input parameter ``Use years in output instead of seconds'' is set, in
  # which case we interpret the formula expressions as having units m/year.
  # 
  # Likewise, since the symbol $t$ indicating time may appear in the formulas
  # for the prescribed velocities, it is interpreted as having units seconds
  # unless the global parameter above has been set.
  # 
  # `gplates': Implementation of a model in which the boundary velocity is
  # derived from files that are generated by the GPlates program.
  # 
  # `zero velocity': Implementation of a model in which the boundary velocity
  # is zero. This is commonly referred to as a ``stick boundary condition'',
  # indicating that the material ``sticks'' to the material on the other side
  # of the boundary.
  set Prescribed velocity boundary indicators = left: function, top:function # default: 

  # A comma separated list of names denoting those boundaries on which the
  # velocity is tangential and unrestrained, i.e., free-slip where no external
  # forces act to prescribe a particular tangential velocity (although there
  # is a force that requires the flow to be tangential).
  # 
  # The names of the boundaries listed here can either by numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  set Tangential velocity boundary indicators = 

  # A comma separated list of names denoting those boundaries on which the
  # velocity is zero.
  # 
  # The names of the boundaries listed here can either by numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  set Zero velocity boundary indicators       = 


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-velocity/ascii-data/test/

    # The file name of the model data. Provide file in format: (File
    # name).\%s\%d, where \%s is a string specifying the boundary of the model
    # according to the names of the boundary indicators (of the chosen
    # geometry model), and \%d is any sprintf integer qualifier specifying the
    # format of the current file number.
    set Data file name             = box_2d_%s.%d.txt

    # Time step between following data files. Depending on the setting of the
    # global `Use years in output instead of seconds' flag in the input file,
    # this number is either interpreted as seconds or as years. The default is
    # one million, i.e., either one million seconds or one million years.
    set Data file time step        = 1e6

    # In some cases the boundary files are not numbered in increasing but in
    # decreasing order (e.g. `Ma BP'). If this flag is set to `True' the
    # plugin will first load the file with the number `First data file number'
    # and decrease the file number during the model run.
    set Decreasing file order      = false

    # Time from which on the data file with number `First data file number' is
    # used as boundary condition. Until this time, a boundary condition equal
    # to zero everywhere is assumed. Depending on the setting of the global
    # `Use years in output instead of seconds' flag in the input file, this
    # number is either interpreted as seconds or as years.
    set First data file model time = 0

    # Number of the first velocity file to be loaded when the model time is
    # larger than `First velocity file model time'.
    set First data file number     = 0

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor               = 1.

    # Specify velocity as r, phi, and theta components instead of x, y, and z.
    # Positive velocities point up, east, and north (in 3D) or out and
    # clockwise (in 2D). This setting only makes sense for spherical
    # geometries.
    set Use spherical unit vectors = false
  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system          = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants         = H=6.0e5, v=0.035355339, eps=0.01, width=50000                                                                                                                                                                      # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression        = if( x<=(H-y)+eps, v, if(x<=(H-y)+width*sqrt(2), v*(0.5 * (1 + cos(pi*(x-(H-y))/(width*sqrt(2))))), 0.0)); if( x<=(H-y)+eps,-v, if(x<=(H-y)+width*sqrt(2),-v*(0.5 * (1 + cos(pi*(x-(H-y))/(width*sqrt(2))))), 0.0)) # default: 0; 0

    # Specify velocity as $r$, $\phi$, and $\theta$ components instead of $x$,
    # $y$, and $z$. Positive velocities point up, east, and north (in 3D) or
    # out and clockwise (in 2D). This setting only makes sense for spherical
    # geometries.
    set Use spherical unit vectors = false

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names             = x,y,t
  end

  subsection GPlates model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a '/') or relative to the current
    # directory. The path may also include the special text
    # '$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-velocity/gplates/

    # Time step between following velocity files. Depending on the setting of
    # the global 'Use years in output instead of seconds' flag in the input
    # file, this number is either interpreted as seconds or as years. The
    # default is one million, i.e., either one million seconds or one million
    # years.
    set Data file time step        = 1e6

    # In some cases the boundary files are not numbered in increasing but in
    # decreasing order (e.g. 'Ma BP'). If this flag is set to 'True' the
    # plugin will first load the file with the number 'First velocity file
    # number' and decrease the file number during the model run.
    set Decreasing file order      = false

    # Time from which on the velocity file with number 'First velocity file
    # number' is used as boundary condition. Previous to this time, a no-slip
    # boundary condition is assumed. Depending on the setting of the global
    # 'Use years in output instead of seconds' flag in the input file, this
    # number is either interpreted as seconds or as years.
    set First data file model time = 0.

    # Number of the first velocity file to be loaded when the model time is
    # larger than 'First velocity file model time'.
    set First data file number     = 0

    # Determines the depth of the lithosphere, so that the GPlates velocities
    # can be applied at the sides of the model as well as at the surface.
    set Lithosphere thickness      = 100000.

    # Point that determines the plane in which a 2D model lies in. Has to be
    # in the format `a,b' where a and b are theta (polar angle) and phi in
    # radians. This value is not utilized in 3D geometries, and can therefore
    # be set to the default or any user-defined quantity.
    set Point one                  = 1.570796,0.0

    # Point that determines the plane in which a 2D model lies in. Has to be
    # in the format `a,b' where a and b are theta (polar angle) and phi in
    # radians. This value is not utilized in 3D geometries, and can therefore
    # be set to the default or any user-defined quantity.
    set Point two                  = 1.570796,1.570796

    # Scalar factor, which is applied to the boundary velocity. You might want
    # to use this to scale the velocities to a reference model (e.g. with
    # free-slip boundary) or another plate reconstruction.
    set Scale factor               = 1.

    # The file name of the material data. Provide file in format: (Velocity
    # file name).\%d.gpml where \%d is any sprintf integer qualifier,
    # specifying the format of the current file number.
    set Velocity file name         = phi.%d
  end

end


subsection Checkpointing
  # The number of timesteps between performing checkpoints. If 0 and time
  # between checkpoint is not specified, checkpointing will not be performed.
  # Units: None.
  set Steps between checkpoint = 200 # default: 0

  # The wall time between performing checkpoints. If 0, will use the
  # checkpoint step frequency instead. Units: Seconds.
  set Time between checkpoint  = 0
end


subsection Compositional fields
  # A comma separated list denoting the solution method of each compositional
  # field. Each entry of the list must be one of the currently implemented
  # field types.
  # 
  # These choices correspond to the following methods by which compositional
  # fields gain their values:\begin{itemize}\item ``field'': If a
  # compositional field is marked with this method, then its values are
  # computed in each time step by advecting along the values of the previous
  # time step using the velocity field, and applying reaction rates to it. In
  # other words, this corresponds to the usual notion of a composition field
  # as mentioned in Section~\ref{sec:compositional}.
  # \item ``particles'': If a compositional field is marked with this method,
  # then its values are obtained in each time step by interpolating the
  # corresponding properties from the particles located on each cell. The time
  # evolution therefore happens because particles move along with the velocity
  # field, and particle properties can react with each other as well. See
  # Section~\ref{sec:particles} for more information about how particles
  # behave.
  # \item ``volume of fluid``: If a compositional field is marked with this
  # method, then its values are obtained in each timestep by reconstructing a
  # polynomial finite element approximation on each cell from a volume of
  # fluid interface tracking method, which is used to compute the advection
  # updates.
  # \item ``static'': If a compositional field is marked this way, then it
  # does not evolve at all. Its values are simply set to the initial
  # conditions, and will then never change.
  # \item ``melt field'': If a compositional field is marked with this method,
  # then its values are computed in each time step by advecting along the
  # values of the previous time step using the melt velocity, and applying
  # reaction rates to it. In other words, this corresponds to the usual notion
  # of a composition field as mentioned in Section~\ref{sec:compositional},
  # except that it is advected with the melt velocity instead of the solid
  # velocity. This method can only be chosen if melt transport is active in
  # the model.
  # \item ``prescribed field'': The value of these fields is determined in
  # each time step from the material model. If a compositional field is marked
  # with this method, then the value of a specific additional material model
  # output, called the `PrescribedFieldOutputs' is interpolated onto the
  # field. This field does not change otherwise, it is not advected with the
  # flow.
  # \item ``prescribed field with diffusion'': If a compositional field is
  # marked this way, the value of a specific additional material model output,
  # called the `PrescribedFieldOutputs' is interpolated onto the field, as in
  # the ``prescribed field'' method. Afterwards, the field is diffused based
  # on a solver parameter, the diffusion length scale, smoothing the field.
  # Specifically, the field is updated by solving the equation $(I-l^2 \Delta)
  # C_\text{smoothed} = C_\text{prescribed}$, where $l$ is the diffusion
  # length scale. Note that this means that the amount of diffusion is
  # independent of the time step size, and that the field is not advected with
  # the flow.\end{itemize}
  set Compositional field methods = 

  # A list of integers smaller than or equal to the number of compositional
  # fields. All compositional fields in this list will be normalized before
  # the first timestep. The normalization is implemented in the following way:
  # First, the sum of the fields to be normalized is calculated at every point
  # and the global maximum is determined. Second, the compositional fields to
  # be normalized are divided by this maximum.
  set List of normalized fields   = 

  # A comma separated list denoting the particle properties that will be
  # projected to those compositional fields that are of the ``particles''
  # field type.
  # 
  # The format of valid entries for this parameter is that of a map given as
  # ``key1: value1, key2: value2 [component2], key3: value3 [component4],
  # ...'' where each key must be a valid field name of the ``particles'' type,
  # and each value must be one of the currently selected particle properties.
  # Component is a component index of the particle property that is 0 by
  # default, but can be set up to n-1, where n is the number of vector
  # components of this particle property. The component indicator only needs
  # to be set if not the first component of the particle property should be
  # mapped (e.g. the $y$-component of the velocity at the particle
  # positions).
  set Mapped particle properties  = 

  # A user-defined name for each of the compositional fields requested.
  set Names of fields             = 

  # The number of fields that will be advected along with the flow field,
  # excluding velocity, pressure and temperature.
  set Number of fields            = 0
end


subsection Discretization
  # The polynomial degree to use for the composition variable(s). As an
  # example, a value of 2 for this parameter will yield either the element
  # $Q_2$ or $DGQ_2$ for the compositional field(s), depending on whether we
  # use continuous or discontinuous field(s).
  # 
  # For continuous elements, the value needs to be 1 or larger as $Q_1$ is the
  # lowest order element, while $DGQ_0$ is a valid choice. Units: None.
  set Composition polynomial degree                = 2

  # The polynomial degree to use for the velocity variables in the Stokes
  # system. The polynomial degree for the pressure variable will then be one
  # less in order to make the velocity/pressure pair conform with the usual
  # LBB (Babu{\v s}ka-Brezzi) condition. In other words, we are using a
  # Taylor-Hood element for the Stokes equations and this parameter indicates
  # the polynomial degree of it. As an example, a value of 2 for this
  # parameter will yield the element $Q_2^d \times Q_1$ for the $d$ velocity
  # components and the pressure, respectively (unless the `Use locally
  # conservative discretization' parameter is set, which modifies the pressure
  # element).
  # 
  # Be careful if you choose 1 as the degree. The resulting element is not
  # stable and it may lead to artifacts in the solution. Units: None.
  set Stokes velocity polynomial degree            = 2

  # The polynomial degree to use for the temperature variable. As an example,
  # a value of 2 for this parameter will yield either the element $Q_2$ or
  # $DGQ_2$ for the temperature field, depending on whether we use a
  # continuous or discontinuous field. Units: None.
  set Temperature polynomial degree                = 2

  # Whether to use a composition discretization that is discontinuous as
  # opposed to continuous. This then requires the assembly of face terms
  # between cells, and weak imposition of boundary terms for the composition
  # field via the discontinuous Galerkin method.
  set Use discontinuous composition discretization = false

  # Whether to use a temperature discretization that is discontinuous as
  # opposed to continuous. This then requires the assembly of face terms
  # between cells, and weak imposition of boundary terms for the temperature
  # field via the interior-penalty discontinuous Galerkin method.
  set Use discontinuous temperature discretization = false

  # By default (i.e., when this parameter is set to its default value `false')
  # \aspect{} uses finite element combinations in which the pressure shape
  # functions are polynomials one degree lower than the shape functions for
  # the velocity. An example is the Taylor-Hood element that uses $Q_k$
  # elements for the velocity and $Q_{k-1}$ for the pressure. This is because
  # using the \textit{same} polynomial degree for both the velocity and the
  # pressure turns out to violate some mathematical properties necessary to
  # make the problem solvable. (In particular, thecondition in question goes
  # by the name ``inf-sup'' or Babu{\v s}ka-Brezzi or LBB condition.) A
  # consequence of violating this condition is that the pressure may show
  # oscillations and not converge to the correct pressure.
  # 
  # That said, people have often used $Q_1$ elements for both thevelocity and
  # pressure anyway. This is commonly referred to as using the Q1-Q1 method.
  # It is, by default, not stable as mentioned above, but it can be made
  # stable by adding small amount of compressibility to the model. There are
  # numerous ways to do that. Today, the way that is generally considered to
  # be the best approach is the one by Dohrmann and Bochev
  # \cite{DohrmannBochev2004}.
  # 
  # When this parameter is set to ``true'', then \aspect{} will use this
  # method by using $Q_k	imes Q_k$ elements for velocity and pressure,
  # respectively, where $k$ is the value provided for the parameter ``Stokes
  # velocity polynomial degree''.
  # 
  # \note{While \aspect{} \textit{allows} you to use this   method, it is
  # generally understood that this is not a   great idea as it leads to rather
  # low accuracy in   general. It also leads to substantial problems when
  # using free surfaces. As a consequence, the presence   of this parameter
  # should not be seen as an   endorsement of the method, or a suggestion to
  # actually use it. It simply makes the method available.}
  set Use equal order interpolation for Stokes     = false

  # Whether to use a Stokes discretization that is locally conservative at the
  # expense of a larger number of degrees of freedom (true), or to go with a
  # cheaper discretization that does not locally conserve mass, although it is
  # globally conservative (false).
  # 
  # When using a locally conservative discretization, the finite element space
  # for the pressure is discontinuous between cells and is the polynomial
  # space $P_{-(k-1)}$ of polynomials of degree $k-1$ in each variable
  # separately. Here, $k$ is the value given in the parameter ``Stokes
  # velocity polynomial degree'', and consequently the polynomial degree for
  # the pressure, $k-1$, is one lower than that for the velocity.
  # 
  # As a consequence of choosing this element for the pressure rather than the
  # more commonly used $Q_{k-1}$ element that is continuous, it can be shown
  # that if the medium is considered incompressible then the computed discrete
  # velocity field $\mathbf u_h$ satisfies the property $\int_ {\partial K}
  # \mathbf u_h \cdot \mathbf n = 0$ for every cell $K$, i.e., for each cell
  # inflow and outflow exactly balance each other as one would expect for an
  # incompressible medium. In other words, the velocity field is
  # \textit{locally conservative}.
  # 
  # On the other hand, if this parameter is set to ``false''(the default),
  # then the finite element space is chosen as $Q_{k-1}$. This choice does not
  # yield the local conservation property but has the advantage of requiring
  # fewer degrees of freedom. Furthermore, the error is generally smaller with
  # this choice.
  # 
  # For an in-depth discussion of these issues and a quantitative evaluation
  # of the different choices, see \cite{KHB12}.
  set Use locally conservative discretization      = true  # default: false


  subsection Stabilization parameters
    # The value used to penalize discontinuities in the discontinuous Galerkin
    # method. This is used only for the temperature field, and not for the
    # composition field, as pure advection does not use the interior penalty
    # method. This is largely empirically decided -- it must be large enough
    # to ensure the bilinear form is coercive, but not so large as to penalize
    # discontinuity at all costs.
    set Discontinuous penalty                              = 10.

    # The maximum global composition values that will be used in the bound
    # preserving limiter for the discontinuous solutions from composition
    # advection fields. The number of the input 'Global composition maximum'
    # values separated by ',' has to be one or the same as the number of the
    # compositional fields. When only one value is supplied, this same value
    # is assumed for all compositional fields.
    set Global composition maximum                         = 1.7976931348623157e+308

    # The minimum global composition value that will be used in the bound
    # preserving limiter for the discontinuous solutions from composition
    # advection fields. The number of the input 'Global composition minimum'
    # values separated by ',' has to be one or the same as the number of the
    # compositional fields. When only one value is supplied, this same value
    # is assumed for all compositional fields.
    set Global composition minimum                         = -1.7976931348623157e+308

    # The maximum global temperature value that will be used in the bound
    # preserving limiter for the discontinuous solutions from temperature
    # advection fields.
    set Global temperature maximum                         = 1.7976931348623157e+308

    # The minimum global temperature value that will be used in the bound
    # preserving limiter for the discontinuous solutions from temperature
    # advection fields.
    set Global temperature minimum                         = -1.7976931348623157e+308

    # Select the method for stabilizing the advection equation. The original
    # method implemented is 'entropy viscosity' as described in \cite {KHB12}.
    # SUPG is currently experimental.
    set Stabilization method                               = entropy viscosity

    # If set to false, the artificial viscosity of a cell is computed and is
    # computed on every cell separately as discussed in \cite{KHB12}. If set
    # to true, the maximum of the artificial viscosity in the cell as well as
    # the neighbors of the cell is computed and used instead.
    set Use artificial viscosity smoothing                 = false

    # Whether to apply the bound preserving limiter as a correction after
    # having the discontinuous composition solution. Currently we apply this
    # only to the compositional solution if the 'Global composition maximum'
    # and 'Global composition minimum' are already defined in the .prm file.
    # This limiter keeps the discontinuous solution in the range given by
    # Global composition maximum' and 'Global composition minimum'.
    set Use limiter for discontinuous composition solution = false

    # Whether to apply the bound preserving limiter as a correction after
    # computing the discontinuous temperature solution. Currently we apply
    # this only to the temperature solution if the 'Global temperature
    # maximum' and 'Global temperature minimum' are already defined in the
    # .prm file. This limiter keeps the discontinuous solution in the range
    # given by 'Global temperature maximum' and 'Global temperature minimum'.
    set Use limiter for discontinuous temperature solution = false

    # The exponent $\alpha$ in the entropy viscosity stabilization. Valid
    # options are 1 or 2. The recommended setting is 2. (This parameter does
    # not correspond to any variable in the 2012 paper by Kronbichler, Heister
    # and Bangerth that describes ASPECT, see \cite{KHB12}. Rather, the paper
    # always uses 2 as the exponent in the definition of the entropy,
    # following equation (15) of the paper. The full approach is discussed in
    # \cite{GPP11}.) Note that this is not the thermal expansion coefficient,
    # also commonly referred to as $\alpha$.Units: None.
    set alpha                                              = 2

    # The $\beta$ factor in the artificial viscosity stabilization. This
    # parameter controls the maximum dissipation of the entropy viscosity,
    # which is the part that only scales with the cell diameter and the
    # maximum velocity in the cell, but does not depend on the solution field
    # itself or its residual. An appropriate value for 2d is 0.052 and 0.78
    # for 3d. (For historical reasons, the name used here is different from
    # the one used in the 2012 paper by Kronbichler, Heister and Bangerth that
    # describes ASPECT, see \cite{KHB12}. This parameter can be given as a
    # single value or as a list with as many entries as one plus the number of
    # compositional fields. In the former case all advection fields use the
    # same stabilization parameters, in the latter case each field
    # (temperature first, then all compositions) use individual parameters.
    # This can be useful to reduce the stabilization for the temperature,
    # which already has some physical diffusion. This parameter corresponds to
    # the factor $\alpha_{\text{max}}$ in the formulas following equation (15)
    # of the paper.) Units: None.
    set beta                                               = 0.052

    # The $c_R$ factor in the entropy viscosity stabilization. This parameter
    # controls the part of the entropy viscosity that depends on the solution
    # field itself and its residual in addition to the cell diameter and the
    # maximum velocity in the cell. This parameter can be given as a single
    # value or as a list with as many entries as one plus the number of
    # compositional fields. In the former case all advection fields use the
    # same stabilization parameters, in the latter case each field
    # (temperature first, then all compositions) use individual parameters.
    # This can be useful to reduce the stabilization for the temperature,
    # which already has some physical diffusion. (For historical reasons, the
    # name used here is different from the one used in the 2012 paper by
    # Kronbichler, Heister and Bangerth that describes ASPECT, see
    # \cite{KHB12}. This parameter corresponds to the factor $\alpha_E$ in the
    # formulas following equation (15) of the paper.) Units: None.
    set cR                                                 = 0.11

    # The strain rate scaling factor in the artificial viscosity
    # stabilization. This parameter determines how much the strain rate (in
    # addition to the velocity) should influence the stabilization. (This
    # parameter does not correspond to any variable in the 2012 paper by
    # Kronbichler, Heister and Bangerth that describes ASPECT, see
    # \cite{KHB12}. Rather, the paper always uses 0, i.e. they specify the
    # maximum dissipation $\nu_h^\text{max}$ as $\nu_h^\text{max}\vert_K =
    # \alpha_{\text{max}} h_K \|\mathbf u\|_{\infty,K}$. Here, we use
    # $\|\lvert\mathbf u\rvert + \gamma h_K \lvert\varepsilon (\mathbf
    # u)\rvert\|_{\infty,K}$ instead of $\|\mathbf u\|_{\infty,K}$. Units:
    # None.
    set gamma                                              = 0.0
  end

end


subsection Formulation
  # Whether to ask the material model for additional terms for the right-hand
  # side of the Stokes equation. This feature is likely only used when
  # implementing force vectors for manufactured solution problems and requires
  # filling additional outputs of type AdditionalMaterialOutputsStokesRHS.
  set Enable additional Stokes RHS = false

  # Whether to include the additional elastic terms on the right-hand side of
  # the Stokes equation.
  set Enable elasticity            = false

  # Whether to include additional terms on the right-hand side of the Stokes
  # equation to set a given compression term specified in the MaterialModel
  # output PrescribedPlasticDilation.
  set Enable prescribed dilation   = false

  # Select a formulation for the basic equations. Different published
  # formulations are available in ASPECT (see the list of possible values for
  # this parameter in the manual for available options). Two ASPECT specific
  # options are
  # \begin{enumerate}
  # \item `isentropic compression': ASPECT's original formulation, using the
  # explicit compressible mass equation, and the full density for the
  # temperature equation.
  # \item `custom': A custom selection of `Mass conservation' and `Temperature
  # equation'.
  # \end{enumerate}
  # 
  # \note{Warning: The `custom' option is implemented for advanced users that
  # want full control over the equations solved. It is possible to choose
  # inconsistent formulations and no error checking is performed on the
  # consistency of the resulting equations.}
  # 
  # \note{The `anelastic liquid approximation' option here can also be used to
  # set up the `truncated anelastic liquid approximation' as long as this
  # option is chosen together with a material model that defines a density
  # that depends on temperature and depth and not on the pressure.}
  set Formulation                  = Boussinesq approximation # default: custom

  # Possible approximations for the density derivatives in the mass
  # conservation equation. Note that this parameter is only evaluated if
  # `Formulation' is set to `custom'. Other formulations ignore the value of
  # this parameter.
  set Mass conservation            = ask material model

  # Possible approximations for the density in the temperature equation.
  # Possible approximations are `real density' and `reference density
  # profile'. Note that this parameter is only evaluated if `Formulation' is
  # set to `custom'. Other formulations ignore the value of this parameter.
  set Temperature equation         = real density
end


subsection Geometry model
  # Select one of the following models:
  # 
  # `box': A box geometry parallel to the coordinate directions. The extent of
  # the box in each coordinate direction is set in the parameter file. The box
  # geometry labels its 2*dim sides as follows: in 2d, boundary indicators 0
  # through 3 denote the left, right, bottom and top boundaries; in 3d,
  # boundary indicators 0 through 5 indicate left, right, front, back, bottom
  # and top boundaries (see also the documentation of the deal.II class
  # ``GeometryInfo''). You can also use symbolic names ``left'', ``right'',
  # etc., to refer to these boundaries in input files. It is also possible to
  # add initial topography to the box model. Note however that this is done
  # after the last initial adaptive refinement cycle. Also, initial topography
  # is supposed to be small, as it is not taken into account when depth or a
  # representative point is computed.
  # 
  # `box with lithosphere boundary indicators': A box geometry parallel to the
  # coordinate directions. The extent of the box in each coordinate direction
  # is set in the parameter file. This geometry model labels its sides with
  # 2*dim+2*(dim-1) boundary indicators: in 2d, boundary indicators 0 through
  # 3 denote the left, right, bottom and top boundaries, while indicators4 and
  # 5 denote the upper part of the left and right vertical boundary,
  # respectively. In 3d, boundary indicators 0 through 5 indicate left, right,
  # front, back, bottom and top boundaries (see also the documentation of the
  # deal.II class ``GeometryInfo''), while indicators 6, 7, 8 and 9 denote the
  # left, right, front and back upper parts of the vertical boundaries,
  # respectively. You can also use symbolic names ``left'', ``right'', ``left
  # lithosphere'', etc., to refer to these boundaries in input files.
  # 
  # Note that for a given ``Global refinement level'' and no user-specified
  # ``Repetitions'', the lithosphere part of the mesh will be more refined.
  # 
  # The additional boundary indicators for the lithosphere allow for selecting
  # boundary conditions for the lithosphere different from those for the
  # underlying mantle. An example application of this geometry is to prescribe
  # a velocity on the lithospheric plates, but use open boundary conditions
  # underneath.
  # 
  # `chunk': A geometry which can be described as a chunk of a spherical
  # shell, bounded by lines of longitude, latitude and radius. The minimum and
  # maximum longitude, latitude (if in 3d) and depth of the chunk is set in
  # the parameter file. The chunk geometry labels its 2*dim sides as follows:
  # ``west'' and ``east'': minimum and maximum longitude, ``south'' and
  # ``north'': minimum and maximum latitude, ``inner'' and ``outer'': minimum
  # and maximum radii.
  # 
  # The dimensions of the model are specified by parameters of the following
  # form: Chunk (minimum || maximum) (longitude || latitude): edges of
  # geographical quadrangle (in degrees)Chunk (inner || outer) radius: Radii
  # at bottom and top of chunk(Longitude || Latitude || Radius) repetitions:
  # number of cells in each coordinate direction.
  # 
  # When used in 2d, this geometry does not imply the use of a spherical
  # coordinate system. Indeed, in 2d the geometry is simply a sector of an
  # annulus in a Cartesian coordinate system and consequently would correspond
  # to a sector of a cross section of the fluid filled space between two
  # infinite cylinders where one has made the assumption that the velocity in
  # direction of the cylinder axes is zero. This is consistent with the
  # definition of what we consider the two-dimension case given in
  # Section~\ref{sec:meaning-of-2d}. It is also possible to add initial
  # topography to the chunk geometry, based on an ascii data file.
  # 
  # `ellipsoidal chunk': A 3D chunk geometry that accounts for Earth's
  # ellipticity (default assuming the WGS84 ellipsoid definition) which can be
  # defined in non-coordinate directions. In the description of the
  # ellipsoidal chunk, two of the ellipsoidal axes have the same length so
  # that there is only a semi-major axis and a semi-minor axis. The user has
  # two options for creating an ellipsoidal chunk geometry: 1) by defining two
  # opposing points (SW and NE or NW and SE) a coordinate parallel ellipsoidal
  # chunk geometry will be created. 2) by defining three points a
  # non-coordinate parallel ellipsoidal chunk will be created. The points are
  # defined in the input file by longitude:latitude. It is also possible to
  # define additional subdivisions of the mesh in each direction. The boundary
  # of the domain is formed by linear interpolation in longitude-latitude
  # space between adjacent points (i.e. [lon, lat](f) = [lon1*f + lon2*(1-f),
  # lat1*f + lat2*(1-f)], where f is a value between 0 and 1). Faces of the
  # model are defined as 0, west; 1,east; 2, south; 3, north; 4, inner; 5,
  # outer.
  # 
  # This geometry model supports initial topography for deforming the initial
  # mesh.
  # 
  # `sphere': A geometry model for a sphere with a user specified radius. This
  # geometry has only a single boundary, so the only valid boundary indicator
  # to specify in input files is ``0''. It can also be referenced by the
  # symbolic name ``surface'' in input files.
  # 
  # Despite the name, this geometry does not imply the use of a spherical
  # coordinate system when used in 2d. Indeed, in 2d the geometry is simply a
  # circle in a Cartesian coordinate system and consequently would correspond
  # to a cross section of the fluid filled interior of an infinite cylinder
  # where one has made the assumption that the velocity in direction of the
  # cylinder axes is zero. This is consistent with the definition of what we
  # consider the two-dimension case given in Section~\ref{sec:meaning-of-2d}.
  # 
  # `spherical shell': A geometry representing a spherical shell or a piece of
  # it. Inner and outer radii are read from the parameter file in subsection
  # 'Spherical shell'.
  # 
  # The spherical shell may be generated as per the original code (with
  # respect to the inner and outer radius, and an initial number of cells
  # along circumference) or following a custom mesh scheme: list of radial
  # values or number of slices. A surface mesh is first generated and refined
  # as desired, before it is extruded radially. A list of radial values
  # subdivides the spherical shell at specified radii. The number of slices
  # subdivides the spherical shell into N slices of equal thickness. The
  # custom spherical shell only works with an opening angle of 360 degrees.
  # 
  # Despite the name, this geometry does not imply the use of a spherical
  # coordinate system when used in 2d. Indeed, in 2d the geometry is simply an
  # annulus in a Cartesian coordinate system and consequently would correspond
  # to a cross section of the fluid filled space between two infinite
  # cylinders where one has made the assumption that the velocity in direction
  # of the cylinder axes is zero. This is consistent with the definition of
  # what we consider the two-dimension case given in
  # Section~\ref{sec:meaning-of-2d}.
  # 
  # The model assigns boundary indicators as follows: In 2d, inner and outer
  # boundaries get boundary indicators zero and one, and if the opening angle
  # set in the input file is less than 360, then left and right boundaries are
  # assigned indicators two and three. These boundaries can also be referenced
  # using the symbolic names `inner', `outer' and (if applicable) `left',
  # `right'.
  # 
  # In 3d, inner and outer indicators are treated as in 2d. If the opening
  # angle is chosen as 90 degrees, i.e., the domain is the intersection of a
  # spherical shell and the first octant, then indicator 2 is at the face
  # $x=0$, 3 at $y=0$, and 4 at $z=0$. These last three boundaries can then
  # also be referred to as `east', `west' and `south' symbolically in input
  # files.
  set Model name = box # default: unspecified


  subsection Box
    # X coordinate of box origin. Units: \si{\meter}.
    set Box origin X coordinate = 0.

    # Y coordinate of box origin. Units: \si{\meter}.
    set Box origin Y coordinate = 0.

    # Z coordinate of box origin. This value is ignored if the simulation is
    # in 2d. Units: \si{\meter}.
    set Box origin Z coordinate = 0.

    # Extent of the box in x-direction. Units: \si{\meter}.
    set X extent                = 6.6e5 # default: 1.

    # Whether the box should be periodic in X direction
    set X periodic              = false

    # Number of cells in X direction.
    set X repetitions           = 66    # default: 1

    # Extent of the box in y-direction. Units: \si{\meter}.
    set Y extent                = 6.0e5 # default: 1.

    # Whether the box should be periodic in Y direction
    set Y periodic              = false

    # Number of cells in Y direction.
    set Y repetitions           = 60    # default: 1

    # Extent of the box in z-direction. This value is ignored if the
    # simulation is in 2d. Units: \si{\meter}.
    set Z extent                = 1.

    # Whether the box should be periodic in Z direction
    set Z periodic              = false

    # Number of cells in Z direction.
    set Z repetitions           = 1
  end

  subsection Box with lithosphere boundary indicators
    # X coordinate of box origin. Units: \si{\meter}.
    set Box origin X coordinate   = 0.

    # Y coordinate of box origin. Units: \si{\meter}.
    set Box origin Y coordinate   = 0.

    # Z coordinate of box origin. This value is ignored if the simulation is
    # in 2d. Units: \si{\meter}.
    set Box origin Z coordinate   = 0.

    # The thickness of the lithosphere used to create additional boundary
    # indicators to set specific boundary conditions for the lithosphere.
    set Lithospheric thickness    = 0.2

    # Extent of the box in x-direction. Units: \si{\meter}.
    set X extent                  = 1.

    # Whether the box should be periodic in X direction.
    set X periodic                = false

    # Whether the box should be periodic in X direction in the lithosphere.
    set X periodic lithosphere    = false

    # Number of cells in X direction of the lower box. The same number of
    # repetitions will be used in the upper box.
    set X repetitions             = 1

    # Extent of the box in y-direction. Units: \si{\meter}.
    set Y extent                  = 1.

    # Whether the box should be periodic in Y direction.
    set Y periodic                = false

    # Whether the box should be periodic in Y direction in the lithosphere.
    # This value is ignored if the simulation is in 2d.
    set Y periodic lithosphere    = false

    # Number of cells in Y direction of the lower box. If the simulation is in
    # 3d, the same number of repetitions will be used in the upper box.
    set Y repetitions             = 1

    # Number of cells in Y direction in the lithosphere. This value is ignored
    # if the simulation is in 3d.
    set Y repetitions lithosphere = 1

    # Extent of the box in z-direction. This value is ignored if the
    # simulation is in 2d. Units: \si{\meter}.
    set Z extent                  = 1.

    # Whether the box should be periodic in Z direction. This value is ignored
    # if the simulation is in 2d.
    set Z periodic                = false

    # Number of cells in Z direction of the lower box. This value is ignored
    # if the simulation is in 2d.
    set Z repetitions             = 1

    # Number of cells in Z direction in the lithosphere. This value is ignored
    # if the simulation is in 2d.
    set Z repetitions lithosphere = 1
  end

  subsection Chunk
    # Radius at the bottom surface of the chunk. Units: \si{\meter}.
    set Chunk inner radius      = 0.

    # Maximum latitude of the chunk. This value is ignored if the simulation
    # is in 2d. Units: degrees.
    set Chunk maximum latitude  = 1.

    # Maximum longitude of the chunk. Units: degrees.
    set Chunk maximum longitude = 1.

    # Minimum latitude of the chunk. This value is ignored if the simulation
    # is in 2d. Units: degrees.
    set Chunk minimum latitude  = 0.

    # Minimum longitude of the chunk. Units: degrees.
    set Chunk minimum longitude = 0.

    # Radius at the top surface of the chunk. Units: \si{\meter}.
    set Chunk outer radius      = 1.

    # Number of cells in latitude. This value is ignored if the simulation is
    # in 2d
    set Latitude repetitions    = 1

    # Number of cells in longitude.
    set Longitude repetitions   = 1

    # Number of cells in radius.
    set Radius repetitions      = 1
  end

  subsection Ellipsoidal chunk
    # Bottom depth of model region.
    set Depth                    = 500000.0

    # The number of subdivisions of the coarse (initial) mesh in depth.
    set Depth subdivisions       = 1

    # The number of subdivisions of the coarse (initial) mesh in the East-West
    # direction.
    set East-West subdivisions   = 1

    # Eccentricity of the ellipsoid. Zero is a perfect sphere, default
    # (8.1819190842622e-2) is WGS84.
    set Eccentricity             = 8.1819190842622e-2

    # Longitude:latitude in degrees of the North-East corner point of model
    # region.The North-East direction is positive. If one of the three corners
    # is not provided the missing corner value will be calculated so all faces
    # are parallel.
    set NE corner                = 

    # Longitude:latitude in degrees of the North-West corner point of model
    # region. The North-East direction is positive. If one of the three
    # corners is not provided the missing corner value will be calculated so
    # all faces are parallel.
    set NW corner                = 

    # The number of subdivisions of the coarse (initial) mesh in the
    # North-South direction.
    set North-South subdivisions = 1

    # Longitude:latitude in degrees of the South-East corner point of model
    # region. The North-East direction is positive. If one of the three
    # corners is not provided the missing corner value will be calculated so
    # all faces are parallel.
    set SE corner                = 

    # Longitude:latitude in degrees of the South-West corner point of model
    # region. The North-East direction is positive. If one of the three
    # corners is not provided the missing corner value will be calculated so
    # all faces are parallel.
    set SW corner                = 

    # The semi-major axis (a) of an ellipsoid. This is the radius for a sphere
    # (eccentricity=0). Default WGS84 semi-major axis.
    set Semi-major axis          = 6378137.0
  end

  subsection Initial topography model
    # Select one of the following models:
    # 
    # `ascii data': Implementation of a model in which the surface topography
    # is derived from a file containing data in ascii format. The following
    # geometry models are currently supported: box, chunk. Note the required
    # format of the input data: The first lines may contain any number of
    # comments if they begin with `#', but one of these lines needs to contain
    # the number of grid points in each dimension as for example `# POINTS: 3
    # 3'. The order of the data columns has to be `x', `Topography [m]' in a
    # 2d model and  `x', `y', `Topography [m]' in a 3d model, which means that
    # there has to be a single column containing the topography. Note that the
    # data in the input file needs to be sorted in a specific order: the first
    # coordinate needs to ascend first, followed by the second in order to
    # assign the correct data to the prescribed coordinates. If you use a
    # spherical model, then the assumed grid changes. `x' will be replaced by
    # the azimuth angle in radians  and `y' by the polar angle in radians
    # measured positive from the north pole. The grid will be assumed to be a
    # longitude-colatitude grid. Note that the order of spherical coordinates
    # is `phi', `theta' and not `theta', `phi', since this allows for
    # dimension independent expressions.
    # 
    # `function': Implementation of a model in which the initial topography is
    # described by a function in cartesian or spherical coordinates.
    # 
    # `prm polygon': An initial topography model that defines the initial
    # topography as constant inside each of a set of polygonal parts of the
    # surface. The polygons, and their associated surface elevation, are
    # defined in the `Geometry model/Initial topography/Prm polygon' section.
    # 
    # `zero topography': Implementation of a model in which the initial
    # topography is zero.
    set Model name = zero topography


    subsection Ascii data model
      # The name of a directory that contains the model data. This path may
      # either be absolute (if starting with a `/') or relative to the current
      # directory. The path may also include the special text
      # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
      # the ASPECT source files were located when ASPECT was compiled. This
      # interpretation allows, for example, to reference files located in the
      # `data/' subdirectory of ASPECT.
      set Data directory = $ASPECT_SOURCE_DIR/data/geometry-model/initial-topography-model/ascii-data/test/

      # The file name of the model data.
      set Data file name = box_2d_%s.0.txt

      # Scalar factor, which is applied to the model data. You might want to
      # use this to scale the input to a reference model. Another way to use
      # this factor is to convert units of the input files. For instance, if
      # you provide velocities in cm/yr set this factor to 0.01.
      set Scale factor   = 1.
    end

    subsection Function
      # A selection that determines the assumed coordinate system for the
      # function variables. Allowed values are `cartesian' and `spherical'.
      # `spherical' coordinates are interpreted as r,phi or r,phi,theta in
      # 2D/3D respectively with theta being the polar angle.
      set Coordinate system        = cartesian

      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants       = 

      # The formula that denotes the function you want to evaluate for
      # particular values of the independent variables. This expression may
      # contain any of the usual operations such as addition or
      # multiplication, as well as all of the common functions such as `sin'
      # or `cos'. In addition, it may contain expressions like `if(x>0, 1,
      # -1)' where the expression evaluates to the second argument if the
      # first argument is true, and to the third argument otherwise. For a
      # full overview of possible expressions accepted see the documentation
      # of the muparser library at http://muparser.beltoforion.de/.
      # 
      # If the function you are describing represents a vector-valued function
      # with multiple components, then separate the expressions for individual
      # components by a semicolon.
      set Function expression      = 0

      # The maximum value the topography given by the function can take.
      set Maximum topography value = 2000.

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names           = x,y,t
    end

    subsection Prm polygon
      # Set the topography height and the polygon which should be set to that
      # height. The format is : "The topography height 	extgreater The point
      # list describing a polygon \& The next topography height 	extgreater
      # the next point list describing a polygon." The format for the point
      # list describing the polygon is "x1,y1;x2,y2". For example for two
      # triangular areas of 100 and -100 meters high set: '100 	extgreater
      # 0,0;5,5;0,10 \& -100 	extgreater 10,10;10,15;20,15'. Units of the
      # height are always in meters. The units of the coordinates are
      # dependent on the geometry model. In the box model they are in meters,
      # in the chunks they are in degrees, etc. Please refer to the manual of
      # the individual geometry model to so see how the topography is
      # implemented.
      set Topography parameters = 
    end

  end

  subsection Sphere
    # Radius of the sphere. Units: \si{\meter}.
    set Radius = 6371000.
  end

  subsection Spherical shell
    # The number of cells in circumferential direction that are created in the
    # coarse mesh in 2d. If zero, this number is chosen automatically in a way
    # that produces meshes in which cells have a reasonable aspect ratio for
    # models in which the depth of the mantle is roughly that of the Earth.
    # For planets with much shallower mantles and larger cores, you may want
    # to chose a larger number to avoid cells that are elongated in tangential
    # and compressed in radial direction.
    # 
    # In 3d, the number of cells is computed differently and does not have an
    # easy interpretation. Valid values for this parameter in 3d are 0 (let
    # this class choose), 6, 12 and 96. Other possible values may be discussed
    # in the documentation of the deal.II function GridGenerator::hyper_shell.
    # The parameter is best left at its default in 3d.
    # 
    # In either case, this parameter is ignored unless the opening angle of
    # the domain is 360 degrees. This parameter is also ignored when using a
    # custom mesh subdivision scheme.
    set Cells along circumference  = 0

    # Choose how the spherical shell mesh is generated. By default, a coarse
    # mesh is generated with respect to the inner and outer radius, and an
    # initial number of cells along circumference. In the other cases, a
    # surface mesh is first generated and refined as desired, before it is
    # extruded radially following the specified subdivision scheme.
    set Custom mesh subdivision    = none

    # Initial lateral refinement for the custom mesh subdivision schemes.The
    # number of refinement steps performed on the initial coarse surface mesh,
    # before the surface is extruded radially. This parameter allows the user
    # more control over the ratio between radial and lateral refinement of the
    # mesh.
    set Initial lateral refinement = 0

    # Inner radius of the spherical shell. Units: \si{\meter}.
    # 
    # \note{The default value of 3,481,000 m equals the radius of a sphere
    # with equal volume as Earth (i.e., 6371 km) minus the average depth of
    # the core-mantle boundary (i.e., 2890 km).}
    set Inner radius               = 3481000.

    # List of radial values for the custom mesh scheme. Units: $\si{m}$. A
    # list of radial values subdivides the spherical shell at specified radii.
    # The list must be strictly ascending, and the first value must be greater
    # than the inner radius while the last must be less than the outer
    # radius.
    set List of radial values      = 

    # Number of slices for the custom mesh subdivision scheme. The number of
    # slices subdivides the spherical shell into N slices of equal thickness.
    # Must be greater than 0.
    set Number of slices           = 1

    # Opening angle in degrees of the section of the shell that we want to
    # build. The only opening angles that are allowed for this geometry are
    # 90, 180, and 360 in 2d; and 90 and 360 in 3d. Units: degrees.
    set Opening angle              = 360.

    # Outer radius of the spherical shell. Units: \si{\meter}.
    # 
    # \note{The default value of 6,336,000 m equals the radius of a sphere
    # with equal volume as Earth (i.e., 6371 km) minus the average depth of
    # the mantle-crust interface (i.e., 35 km).}
    set Outer radius               = 6336000.

    # Whether the shell should be periodic in the phi direction.
    set Phi periodic               = false
  end

end


subsection Gravity model
  # Select one of the following models:
  # 
  # `ascii data': Gravity is read from a file that describes the reference
  # state. The default profile follows the preliminary reference Earth model
  # (PREM, Dziewonski and Anderson, 1981). Note the required format of the
  # input data: The first lines may contain any number of comments if they
  # begin with `#', but one of these lines needs to contain the number of
  # points in the reference state as for example `# POINTS: 3'. Following the
  # comment lines there has to be a single line containing the names of all
  # data columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide a column named `gravity'.
  # Note that the data lines in the file need to be sorted in order of
  # increasing depth from 0 to the maximal depth in the model domain. Points
  # in the model that are outside of the provided depth range will be assigned
  # the maximum or minimum depth values, respectively. Points do not need to
  # be equidistant, but the computation of properties is optimized in speed if
  # they are.
  # 
  # `function': Gravity is given in terms of an explicit formula that is
  # elaborated in the parameters in section ``Gravity model|Function''. The
  # format of these functions follows the syntax understood by the muparser
  # library, see Section~\ref{sec:muparser-format}.
  # 
  # `radial constant': A gravity model in which the gravity has a constant
  # magnitude and the direction is radial (pointing inward if the value is
  # positive). The magnitude is read from the parameter file in subsection
  # 'Radial constant'.
  # 
  # `radial earth-like': This plugin has been removed due to its misleading
  # name. The included profile was hard-coded and was less earth-like than the
  # `ascii data' plugin, which uses the profile of the Preliminary Reference
  # Earth Model (PREM). Use `ascii data' instead of `radial earth-like'.
  # 
  # `radial linear': A gravity model which is radial (pointing inward if the
  # gravity is positive) and the magnitude changes linearly with depth. The
  # magnitude of gravity at the surface and bottom is read from the input file
  # in a section ``Gravity model/Radial linear''.
  # 
  # `vertical': A gravity model in which the gravity direction is vertical
  # (pointing downward for positive values) and at a constant magnitude by
  # default equal to one.
  set Model name = vertical # default: unspecified


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory = $ASPECT_SOURCE_DIR/data/gravity-model/

    # The file name of the model data.
    set Data file name = prem.txt

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor   = 1.
  end

  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Radial constant
    # Magnitude of the gravity vector in $m/s^2$. For positive values the
    # direction is radially inward towards the center of the earth.
    set Magnitude = 9.81
  end

  subsection Radial linear
    # Magnitude of the radial gravity vector at the bottom of the domain.
    # `Bottom' means themaximum depth in the chosen geometry, and for example
    # represents the core-mantle boundary in the case of the `spherical shell'
    # geometry model, and the center in the case of the `sphere' geometry
    # model. Units: \si{\meter\per\second\squared}.
    set Magnitude at bottom  = 10.7

    # Magnitude of the radial gravity vector at the surface of the domain.
    # Units: \si{\meter\per\second\squared}.
    set Magnitude at surface = 9.8
  end

  subsection Vertical
    # Value of the gravity vector in $m/s^2$ directed along negative y (2D) or
    # z (3D) axis (if the magnitude is positive.
    set Magnitude = 0.0 # default: 1.
  end

end


subsection Heating model
  # A comma separated list of heating models that will be used to calculate
  # the heating terms in the energy equation. The results of each of these
  # criteria, i.e., the heating source terms and the latent heat terms for the
  # left hand side will be added.
  # 
  # The following heating models are available:
  # 
  # `adiabatic heating': Implementation of a standard and a simplified model
  # of adiabatic heating.
  # 
  # `adiabatic heating of melt': Implementation of a standard and a simplified
  # model of adiabatic heating of melt. The full model implements the heating
  # term
  # $\alpha T (-\phi \mathbf u_s \cdot \nabla p) + \alpha T (\phi \mathbf u_f
  # \cdot \nabla p)$.
  # For full adiabatic heating, this has to be used in combination with the
  # heating model `adiabatic heating' to also include adiabatic heating for
  # the solid part, and the full heating term is then $\alpha T ((1-\phi)
  # \mathbf u_s \cdot \nabla p) + \alpha T (\phi \mathbf u_f \cdot \nabla p)$.
  # 
  # `compositional heating': Implementation of a model in which magnitude of
  # internal heat production is determined from fixed values assigned to each
  # compositional field. These values are interpreted as having units
  # \si{\watt\per\meter\cubed}.
  # 
  # `constant heating': Implementation of a model in which the heating rate is
  # constant.
  # 
  # `function': Implementation of a model in which the heating rate is given
  # in terms of an explicit formula that is elaborated in the parameters in
  # section ``Heating model|Function''. The format of these functions follows
  # the syntax understood by the muparser library, see
  # Section~\ref{sec:muparser-format}.
  # 
  # The formula is interpreted as having units W/kg.
  # 
  # Since the symbol $t$ indicating time may appear in the formulas for the
  # heating rate, it is interpreted as having units seconds unless the global
  # parameter ``Use years in output instead of seconds'' is set.
  # 
  # `latent heat': Implementation of a standard model for latent heat.
  # 
  # `latent heat melt': Implementation of a standard model for latent heat of
  # melting. This assumes that there is a compositional field called porosity,
  # and it uses the reaction term of this field (the fraction of material that
  # melted in the current time step) multiplied by a constant entropy change
  # for melting all of the material as source term of the heating model.
  # If there is no field called porosity, the heating terms are 0.
  # 
  # `radioactive decay': Implementation of a model in which the internal
  # heating rate is radioactive decaying in the following rule:
  # \[(\text{initial concentration})\cdot 0.5^{\text{time}/(\text{half
  # life})}\]
  # The crust and mantle can have different concentrations, and the crust can
  # be defined either by depth or by a certain compositional field.
  # The formula is interpreted as having units W/kg.
  # 
  # `shear heating': Implementation of a standard model for shear heating.
  # Adds the term: $  2 \eta \left( \varepsilon - \frac{1}{3} \text{tr}
  # \varepsilon \mathbf 1 \right) : \left( \varepsilon - \frac{1}{3} \text{tr}
  # \varepsilon \mathbf 1 \right)$ to the right-hand side of the temperature
  # equation.
  # 
  # `shear heating with melt': Implementation of a standard model for shear
  # heating of migrating melt, including bulk (compression) heating $\xi
  # \left( \nabla \cdot \mathbf u_s \right)^2 $ and heating due to melt
  # segregation $\frac{\eta_f \phi^2}{k} \left( \mathbf u_f - \mathbf u_s
  # \right)^2 $. For full shear heating, this has to be used in combination
  # with the heating model shear heating to also include shear heating for the
  # solid part.
  set List of model names = 


  subsection Adiabatic heating
    # A flag indicating whether the adiabatic heating should be simplified
    # from $\alpha T (\mathbf u \cdot \nabla p)$ to $ \alpha \rho T (\mathbf u
    # \cdot \mathbf g) $.
    set Use simplified adiabatic heating = false
  end

  subsection Adiabatic heating of melt
    # A flag indicating whether the adiabatic heating should be simplified
    # from $\alpha T (\mathbf u \cdot \nabla p)$ to $ \alpha \rho T (\mathbf u
    # \cdot \mathbf g) $.
    set Use simplified adiabatic heating = false
  end

  subsection Compositional heating
    # List of heat production per unit volume values for background and
    # compositional fields, for a total of N+1 values, where the first value
    # corresponds to the background material, and N is the number of
    # compositional fields. Units: \si{\watt\per\meter\cubed}.
    set Compositional heating values                          = 0.

    # A list of integers with as many entries as compositional fields plus
    # one. The first entry corresponds to the background material, each
    # following entry corresponds to a particular compositional field. If the
    # entry for a field is '1' this field is considered during the computation
    # of volume fractions, if it is '0' the field is ignored. This is useful
    # if some compositional fields are used to track properties like finite
    # strain that should not contribute to heat production. The first entry
    # determines whether the background field contributes to heat production
    # or not (essentially similar to setting its 'Compositional heating
    # values' to zero, but included for consistency in the length of the input
    # lists).
    set Use compositional field for heat production averaging = 1
  end

  subsection Constant heating
    # The specific rate of heating due to radioactive decay (or other bulk
    # sources you may want to describe). This parameter corresponds to the
    # variable $H$ in the temperature equation stated in the manual, and the
    # heating term is $
ho H$. Units: W/kg.
    set Radiogenic heating rate = 0.
  end

  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Latent heat melt
    # The entropy change for the phase transition from solid to melt. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Melting entropy change = -300.
  end

  subsection Radioactive decay
    # Which composition field should be treated as crust
    set Crust composition number      = 0

    # Whether crust defined by composition or depth
    set Crust defined by composition  = false

    # Depth of the crust when crust if defined by depth. Units: \si{\meter}.
    set Crust depth                   = 0.

    # Half decay times. Units: (Seconds), or (Years) if set `use years instead
    # of seconds'.
    set Half decay times              = 

    # Heating rates of different elements (W/kg)
    set Heating rates                 = 

    # Initial concentrations of different elements (ppm)
    set Initial concentrations crust  = 

    # Initial concentrations of different elements (ppm)
    set Initial concentrations mantle = 

    # Number of radioactive elements
    set Number of elements            = 0
  end

end


subsection Initial composition model
  # A comma-separated list of initial composition models that together
  # describe the initial composition field. These plugins are loaded in the
  # order given, and modify the existing composition field via the operators
  # listed in 'List of model operators'.
  # 
  # The following composition models are available:
  # 
  # `adiabatic density': Specify the initial composition as the adiabatic
  # reference density at each position. Note that only the field with the name
  # 'density\_field' will be filled for all other fields this plugin returns
  # 0.0.
  # 
  # `ascii data': Implementation of a model in which the initial composition
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `y', `composition1',
  # `composition2', etc. in a 2d model and `x', `y', `z', `composition1',
  # `composition2', etc. in a 3d model, according to the number of
  # compositional fields, which means that there has to be a single column for
  # every composition in the model.Note that the data in the input files need
  # to be sorted in a specific order: the first coordinate needs to ascend
  # first, followed by the second and the third at last in order to assign the
  # correct data to the prescribed coordinates. If you use a spherical model,
  # then the assumed grid changes. `x' will be replaced by the radial distance
  # of the point to the bottom of the model, `y' by the azimuth angle and `z'
  # by the polar angle measured positive from the north pole. The grid will be
  # assumed to be a latitude-longitude grid. Note that the order of spherical
  # coordinates is `r', `phi', `theta' and not `r', `theta', `phi', since this
  # allows for dimension independent expressions.
  # 
  # `ascii data layered': Implementation of a model in which the initial
  # composition is derived from files containing data in ascii format. Each
  # file defines a surface on which compositional fields are defined. Between
  # the surfaces, the fields can be chosen to be constant (with a value
  # defined by the nearest shallower surface), or linearly interpolated
  # between surfaces. Note the required format of the input ascii data file:
  # The first lines may contain any number of comments if they begin with `#',
  # but one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 3 3'. The order of the data columns
  # has to be `x', `y', `composition1', `composition2' etc. in a 2d model and
  # `x', `y', `z', `composition1', `composition2' etc. in a 3d model; i.e. the
  # columns before the compositional field always contains the position of the
  # surface along the vertical direction. The first column needs to ascend
  # first, followed by the second in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the azimuth angle and `y' (if 3D) by
  # the polar angle measured positive from the north pole. The last column
  # will be the distance of the point from the origin (i.e. radial position).
  # The grid in this case will be a latitude-longitude grid. Note that the
  # order of spherical coordinates in 3D is `phi', `theta', `r', `T'and not
  # `theta', `phi', `r', `T' as this is more consistent with other ASPECT
  # plugins. Outside of the region defined by the grid, the plugin will use
  # the value at the edge of the region.
  # 
  # `function': Specify the composition in terms of an explicit formula. The
  # format of these functions follows the syntax understood by the muparser
  # library, see Section~\ref{sec:muparser-format}.
  # 
  # `porosity': A class that implements initial conditions for the porosity
  # field by computing the equilibrium melt fraction for the given initial
  # condition and reference pressure profile. Note that this plugin only works
  # if there is a compositional field called `porosity', and the used material
  # model implements the 'MeltFractionModel' interface. For all compositional
  # fields except porosity this plugin returns 0.0, and they are therefore not
  # changed as long as the default `add' operator is selected for this plugin.
  # 
  # `world builder': Specify the initial composition through the World
  # Builder. More information on the World Builder can be found at
  # \url{https://geodynamicworldbuilder.github.io}. Make sure to specify the
  # location of the World Builder file in the parameter 'World builder file'.
  set List of model names                 = 

  # A comma-separated list of operators that will be used to append the listed
  # composition models onto the previous models. If only one operator is
  # given, the same operator is applied to all models.
  set List of model operators             = add

  # Select one of the following models:
  # 
  # `adiabatic density': Specify the initial composition as the adiabatic
  # reference density at each position. Note that only the field with the name
  # 'density\_field' will be filled for all other fields this plugin returns
  # 0.0.
  # 
  # `ascii data': Implementation of a model in which the initial composition
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `y', `composition1',
  # `composition2', etc. in a 2d model and `x', `y', `z', `composition1',
  # `composition2', etc. in a 3d model, according to the number of
  # compositional fields, which means that there has to be a single column for
  # every composition in the model.Note that the data in the input files need
  # to be sorted in a specific order: the first coordinate needs to ascend
  # first, followed by the second and the third at last in order to assign the
  # correct data to the prescribed coordinates. If you use a spherical model,
  # then the assumed grid changes. `x' will be replaced by the radial distance
  # of the point to the bottom of the model, `y' by the azimuth angle and `z'
  # by the polar angle measured positive from the north pole. The grid will be
  # assumed to be a latitude-longitude grid. Note that the order of spherical
  # coordinates is `r', `phi', `theta' and not `r', `theta', `phi', since this
  # allows for dimension independent expressions.
  # 
  # `ascii data layered': Implementation of a model in which the initial
  # composition is derived from files containing data in ascii format. Each
  # file defines a surface on which compositional fields are defined. Between
  # the surfaces, the fields can be chosen to be constant (with a value
  # defined by the nearest shallower surface), or linearly interpolated
  # between surfaces. Note the required format of the input ascii data file:
  # The first lines may contain any number of comments if they begin with `#',
  # but one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 3 3'. The order of the data columns
  # has to be `x', `y', `composition1', `composition2' etc. in a 2d model and
  # `x', `y', `z', `composition1', `composition2' etc. in a 3d model; i.e. the
  # columns before the compositional field always contains the position of the
  # surface along the vertical direction. The first column needs to ascend
  # first, followed by the second in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the azimuth angle and `y' (if 3D) by
  # the polar angle measured positive from the north pole. The last column
  # will be the distance of the point from the origin (i.e. radial position).
  # The grid in this case will be a latitude-longitude grid. Note that the
  # order of spherical coordinates in 3D is `phi', `theta', `r', `T'and not
  # `theta', `phi', `r', `T' as this is more consistent with other ASPECT
  # plugins. Outside of the region defined by the grid, the plugin will use
  # the value at the edge of the region.
  # 
  # `function': Specify the composition in terms of an explicit formula. The
  # format of these functions follows the syntax understood by the muparser
  # library, see Section~\ref{sec:muparser-format}.
  # 
  # `porosity': A class that implements initial conditions for the porosity
  # field by computing the equilibrium melt fraction for the given initial
  # condition and reference pressure profile. Note that this plugin only works
  # if there is a compositional field called `porosity', and the used material
  # model implements the 'MeltFractionModel' interface. For all compositional
  # fields except porosity this plugin returns 0.0, and they are therefore not
  # changed as long as the default `add' operator is selected for this plugin.
  # 
  # `world builder': Specify the initial composition through the World
  # Builder. More information on the World Builder can be found at
  # \url{https://geodynamicworldbuilder.github.io}. Make sure to specify the
  # location of the World Builder file in the parameter 'World builder file'.
  # 
  # \textbf{Warning}: This parameter provides an old and deprecated way of
  # specifying initial composition models and shouldn't be used. Please use
  # 'List of model names' instead.
  set Model name                          = unspecified

  # A comma separated list denoting the method to be used to initialize a
  # composition field specified to be advected using the volume of fluid
  # method.
  # 
  # The format of valid entries for this parameter is that of a map given as
  # ``key1:value1, key2:value2`` where each key must be the name of a
  # compositional field using the volume of fluid advection method, and the
  # value is one of ``composition`` or ``level set``. ``composition`` is the
  # default
  # 
  # When ``composition is specified, the initial model is treated as a
  # standard composition field with bounds between 0 and 1 assumed, The
  # initial fluid fractions are then based on an iterated midpoint quadrature.
  # Resultant volume fractions outside of the bounds will be coerced to the
  # nearest valid value (ie 0 or 1). If ``level set`` is specified, the intial
  # data will be assumed to be in the form of a signed distance level set
  # function (i.e. a function which is positive when in the fluid, negative
  # outside, and zero on the interface and the magnitude is always the
  # distance to the interface so the gradient is one everywhere).
  set Volume of fluid initialization type = 


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory       = $ASPECT_SOURCE_DIR/data/initial-composition/ascii-data/test/

    # The file name of the model data.
    set Data file name       = initial_composition_top_mantle_box_3d.txt

    # The file names of the model data (comma separated).
    set Data file names      = initial_composition_top_mantle_box_3d.txt

    # Method to interpolate between layer boundaries. Select from piecewise
    # constant or linear. Piecewise constant takes the value from the nearest
    # layer boundary above the data point. The linear option interpolates
    # linearly between layer boundaries. Above and below the domain given by
    # the layer boundaries, the values aregiven by the top and bottom layer
    # boundary.
    set Interpolation scheme = linear

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor         = 1.
  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

end


subsection Initial temperature model
  # A comma-separated list of initial temperature models that will be used to
  # initialize the temperature. These plugins are loaded in the order given,
  # and modify the existing temperature field via the operators listed in
  # 'List of model operators'.
  # 
  # The following initial temperature models are available:
  # 
  # `S40RTS perturbation': An initial temperature field in which the
  # temperature is perturbed following the S20RTS or S40RTS shear wave
  # velocity model by Ritsema and others, which can be downloaded here
  # \url{http://www.earth.lsa.umich.edu/~jritsema/research.html}. Information
  # on the vs model can be found in Ritsema, J., Deuss, A., van Heijst, H.J.
  # \& Woodhouse, J.H., 2011. S40RTS: a degree-40 shear-velocity model for the
  # mantle from new Rayleigh wave dispersion, teleseismic traveltime and
  # normal-mode splitting function measurements, Geophys. J. Int. 184,
  # 1223-1236. The scaling between the shear wave perturbation and the density
  # perturbation can be constant and set by the user with the 'Vs to density
  # scaling' parameter or depth-dependent and read in from a file. To convert
  # density the user can specify the 'Thermal expansion coefficient in initial
  # temperature scaling' parameter. The scaling is as follows: $\delta \ln
  # \rho (r,\theta,\phi) = \xi \cdot \delta \ln v_s(r,\theta, \phi)$ and
  # $\delta T(r,\theta,\phi) = - \frac{1}{\alpha} \delta \ln
  # \rho(r,\theta,\phi)$. $\xi$ is the `vs to density scaling' parameter and
  # $\alpha$ is the 'Thermal expansion coefficient in initial temperature
  # scaling' parameter. The temperature perturbation is added to an otherwise
  # constant temperature (incompressible model) or adiabatic reference profile
  # (compressible model). If a depth is specified in 'Remove temperature
  # heterogeneity down to specified depth', there is no temperature
  # perturbation prescribed down to that depth.
  # Note the required file format if the vs to density scaling is read in from
  # a file: The first lines may contain any number of comments if they begin
  # with '#', but one of these lines needs to contain the number of points in
  # the reference state as for example '# POINTS: 3'. Following the comment
  # lines there has to be a single line containing the names of all data
  # columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide the columns named `depth' and
  # `vs\_to\_density'. Note that the data lines in the file need to be sorted
  # in order of increasing depth from 0 to the maximal depth in the model
  # domain. Points in the model that are outside of the provided depth range
  # will be assigned the maximum or minimum depth values, respectively. Points
  # do not need to be equidistant, but the computation of properties is
  # optimized in speed if they are.
  # If the plugin is used in 2D it will use an equatorial slice of the seismic
  # tomography model.
  # 
  # `SAVANI perturbation': An initial temperature field in which the
  # temperature is perturbed following the SAVANI shear wave velocity model by
  # Auer and others, which can be downloaded here
  # \url{http://n.ethz.ch/~auerl/savani.tar.bz2}. Information on the vs model
  # can be found in Auer, L., Boschi, L., Becker, T.W., Nissen-Meyer, T. \&
  # Giardini, D., 2014. Savani: A variable resolution whole-mantle model of
  # anisotropic shear velocity variations based on multiple data sets. Journal
  # of Geophysical Research: Solid Earth 119.4 (2014): 3006-3034. The scaling
  # between the shear wave perturbation and the density perturbation can be
  # constant and set by the user with the 'Vs to density scaling' parameter or
  # depth-dependent and read in from a file. To convert density the user can
  # specify the 'Thermal expansion coefficient in initial temperature scaling'
  # parameter. The scaling is as follows: $\delta \ln \rho (r,\theta,\phi) =
  # \xi \cdot \delta \ln v_s(r,\theta, \phi)$ and $\delta T(r,\theta,\phi) = -
  # \frac{1}{\alpha} \delta \ln \rho(r,\theta,\phi)$. $\xi$ is the `vs to
  # density scaling' parameter and $\alpha$ is the 'Thermal expansion
  # coefficient in initial temperature scaling' parameter. The temperature
  # perturbation is added to an otherwise constant temperature (incompressible
  # model) or adiabatic reference profile (compressible model).If a depth is
  # specified in 'Remove temperature heterogeneity down to specified depth',
  # there is no temperature perturbation prescribed down to that depth.
  # Note the required file format if the vs to density scaling is read in from
  # a file: The first lines may contain any number of comments if they begin
  # with '#', but one of these lines needs to contain the number of points in
  # the reference state as for example '# POINTS: 3'. Following the comment
  # lines there has to be a single line containing the names of all data
  # columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide the columns named `depth' and
  # `vs\_to\_density'. Note that the data lines in the file need to be sorted
  # in order of increasing depth from 0 to the maximal depth in the model
  # domain. Points in the model that are outside of the provided depth range
  # will be assigned the maximum or minimum depth values, respectively. Points
  # do not need to be equidistant, but the computation of properties is
  # optimized in speed if they are.
  # 
  # `adiabatic': Temperature is prescribed as an adiabatic profile with upper
  # and lower thermal boundary layers, whose ages are given as input
  # parameters.
  # 
  # `adiabatic boundary': An initial temperature condition that allows for
  # discretizing the model domain into two layers separated by a user-defined
  # isothermal boundary. The user includes an input ascii data file that is
  # formatted as 3 columns of `longitude(radians)', `colatitude(radians)', and
  # `isotherm depth(meters)', where `isotherm depth' represents the depth of
  # an initial temperature of 1673.15 K (by default). The first lines in the
  # data file may contain any number of comments if they begin with `#', but
  # one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 69 121'. Note that the coordinates
  # need to be sorted in a specific order: the `longitude' coordinate needs to
  # ascend first, followed by the `colatitude' coordinate in order to assign
  # the correct data (isotherm depth) to the prescribed coordinates. The
  # temperature is defined from the surface (273.15 K) to the isotherm depth
  # (1673.15 K) as a linear gradient. Below the isotherm depth the temperature
  # increases approximately adiabatically (0.0005 K per meter). This plugin
  # should work for all geometry models, but is currently only tested for
  # spherical models.
  # 
  # `ascii data': Implementation of a model in which the initial temperature
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `y', `Temperature [K]' in
  # a 2d model and  `x', `y', `z', `Temperature [K]' in a 3d model, which
  # means that there has to be a single column containing the temperature.
  # Note that the data in the input files need to be sorted in a specific
  # order: the first coordinate needs to ascend first, followed by the second
  # and the third at last in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the radial distance of the point to
  # the bottom of the model, `y' by the azimuth angle and `z' by the polar
  # angle measured positive from the north pole. The grid will be assumed to
  # be a latitude-longitude grid. Note that the order of spherical coordinates
  # is `r', `phi', `theta' and not `r', `theta', `phi', since this allows for
  # dimension independent expressions.
  # 
  # `ascii data layered': Implementation of a model in which the initial
  # temperature is derived from files containing data in ascii format. Each
  # file defines a surface on which temperature is defined. Between the
  # surfaces, the temperatures can be chosen to be constant (with a value
  # defined by the nearest shallower surface), or linearly interpolated
  # between surfaces. Note the required format of the input ascii data file:
  # The first lines may contain any number of comments if they begin with `#',
  # but one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 3 3'. The order of the data columns
  # has to be `x', `y', `Temperature [K]' in a 2d model and `x', `y', `z',
  # `Temperature [K]' in a 3d model; i.e. the last two columns always contain
  # the position of the isotherm along the vertical direction, and the
  # temperature at that point. The first column needs to ascend first,
  # followed by the second in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the azimuth angle and `y' (if 3D) by
  # the polar angle measured positive from the north pole. The last column
  # will be the distance of the point from the origin (i.e. radial position).
  # The grid in this case will be a latitude-longitude grid. Note that the
  # order of spherical coordinates in 3D is `phi', `theta', `r', `T'and not
  # `theta', `phi', `r', `T' as this is more consistent with other ASPECT
  # plugins. Outside of the region defined by the grid, the plugin will use
  # the value at the edge of the region.
  # 
  # `ascii profile': Implementation of a model in which the initial
  # temperature is read from a file that provides these values as a function
  # of depth. Note the required format of the input data: The first lines may
  # contain any number of comments if they begin with `#', but one of these
  # lines needs to contain the number of points in the temperature profile,
  # for example `# POINTS: 10'. Following the comment lines, there has to be a
  # single line containing the names of all data columns, separated by
  # arbitrarily many spaces. Column names are not allowed to contain spaces.
  # The file can contain unnecessary columns, but for this plugin it needs to
  # at least provide columns named `depth' and`temperature'.Note that the data
  # lines in the file need to be sorted in order of increasing depth from 0 to
  # the maximal depth in the model domain. Points in the model that are
  # outside of the provided depth range will be assigned the maximum or
  # minimum depth values, respectively. Points do not need to be equidistant,
  # but the computation of properties is optimized in speed if they are.
  # 
  # `continental geotherm': This is a temperature initial condition that
  # computes a continental geotherm based on the solution of the steady-state
  # conductive equation $k\frac{d^2 T}{dy^2}+\rho H = 0$ as described in e.g.
  # Turcotte and Schubert, Ch. 4.6, or Chapman (1986). As boundary conditions,
  # we take the surface temperature and the temperature of the
  # Lithosphere-Asthenosphere Boundary (LAB).
  # The geotherm is computed for a homogeneous lithosphere composed of an
  # upper crust, lower crust and mantle layer. The crustal layers are assumed
  # to have a constant radioactive heating, and all layers are assumed to have
  # a constant thermal conductivity. Layer thicknesses, surface temperature
  # and LAB temperature should be specified by the user. For consistency, the
  # density, heat production and thermal conductivity of each layer are read
  # from the visco plastic material model and the compositional heating model.
  # 
  # For any depths below the depth of the LAB, a unrealistically high
  # temperature is returned, such that this plugin can be combined with
  # another temperature plugin through the 'minimum' operator.
  # Note that the current implementation only works for a 3-layer lithosphere,
  # even though in principle the heat conduction equation can be solved for
  # any number of layers. The naming of the compositional fields that
  # represent the layers is also very specific, namely `upper\_crust',
  # `lower\_crust', and `lithospheric\_mantle'.
  # Make sure the top and bottom temperatures of the lithosphere agree with
  # temperatures set in for example the temperature boundary conditions.
  # 
  # `function': Specify the initial temperature in terms of an explicit
  # formula. The format of these functions follows the syntax understood by
  # the muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `harmonic perturbation': An initial temperature field in which the
  # temperature is perturbed following a harmonic function (spherical harmonic
  # or sine depending on geometry and dimension) in lateral and radial
  # direction from an otherwise constant temperature (incompressible model) or
  # adiabatic reference profile (compressible model).
  # 
  # `inclusion shape perturbation': An initial temperature field in which
  # there is an inclusion in a constant-temperature box field. The size,
  # shape, gradient, position, and temperature of the inclusion are defined by
  # parameters.
  # 
  # `lithosphere mask': Implementation of a model in which the initial
  # temperature is set to a specified lithosphere temperature above the
  # lithosphere-asthenosphere boundary (specified by an ascii file or maximum
  # lithosphere depth value). Below this the initial temperature is set as
  # NaN.  Note the required format of the input data file: The first lines may
  # contain any number of comments if they begin with '#', but one of these
  # lines needs to contain the number of grid points in each dimension as for
  # example '# POINTS: 3 3'. For a spherical model, the order of the data
  # columns has to be 'phi', 'theta', 'depth (m)', where phi is the azimuth
  # angle and theta is the polar angle measured positive from the north pole.
  # This plug-in can be combined with another using the 'replace if valid'
  # operator.
  # 
  # `mandelbox': Fractal-shaped temperature field.
  # 
  # `patch on S40RTS': Implementation of a model in which the initial
  # temperature is derived from a file containing shear wave velocity
  # perturbations in ascii format (e.g. a high resolution upper mantle
  # tomography) combined with S40RTS. Note the required format of the input
  # ascii input data: The first lines may contain any number of comments if
  # they begin with '#', but one of these lines needs to contain the number of
  # grid points in each dimension as for example '# POINTS: 3 3 3'. The order
  # of the data columns has to be  `x', `y', `z', 'Vs Perturbation' in a 3d
  # model, which means that there has to be a single column containing the
  # temperature. Note that the data in the input files need to be sorted in a
  # specific order: the first coordinate needs to ascend first, followed by
  # the second and the third at last in order to assign the correct data to
  # the prescribed coordinates. In the spherical model data will be handled as
  # Cartesian, however, `x' will be replaced by the radial distance of the
  # point to the bottom of the model, `y' by the azimuth angle and `z' by the
  # polar angle measured positive from the north pole. The grid will be
  # assumed to be a latitude-longitude grid. Note that the order of spherical
  # coordinates is `r', `phi', `theta' and not `r', `theta', `phi', since this
  # allows for dimension independent expressions. See S40RTS documentation for
  # details on input parameters in the S40RTS perturbation subsection. The
  # boundary between the two tomography models is smoothed using a depth
  # weighted combination of Vs values within the region of smoothing.
  # 
  # `perturbed box': An initial temperature field in which the temperature is
  # perturbed slightly from an otherwise constant value equal to one. The
  # perturbation is chosen in such a way that the initial temperature is
  # constant to one along the entire boundary.
  # 
  # `polar box': An initial temperature field in which the temperature is
  # perturbed slightly from an otherwise constant value equal to one. The
  # perturbation is such that there are two poles on opposing corners of the
  # box.
  # 
  # `spherical gaussian perturbation': An initial temperature field in which
  # the temperature is perturbed by a single Gaussian added to an otherwise
  # spherically symmetric state. Additional parameters are read from the
  # parameter file in subsection 'Spherical gaussian perturbation'.
  # 
  # `spherical hexagonal perturbation': An initial temperature field in which
  # the temperature is perturbed following an $N$-fold pattern in a specified
  # direction from an otherwise spherically symmetric state. The class's name
  # comes from previous versions when the only option was $N=6$.
  # 
  # `world builder': Specify the initial temperature through the World
  # Builder. More information on the World Builder can be found at
  # \url{https://geodynamicworldbuilder.github.io}. Make sure to specify the
  # location of the World Builder file in the parameter 'World builder file'.
  set List of model names     = 

  # A comma-separated list of operators that will be used to append the listed
  # temperature models onto the previous models. If only one operator is
  # given, the same operator is applied to all models.
  set List of model operators = add

  # Select one of the following models:
  # 
  # `S40RTS perturbation': An initial temperature field in which the
  # temperature is perturbed following the S20RTS or S40RTS shear wave
  # velocity model by Ritsema and others, which can be downloaded here
  # \url{http://www.earth.lsa.umich.edu/~jritsema/research.html}. Information
  # on the vs model can be found in Ritsema, J., Deuss, A., van Heijst, H.J.
  # \& Woodhouse, J.H., 2011. S40RTS: a degree-40 shear-velocity model for the
  # mantle from new Rayleigh wave dispersion, teleseismic traveltime and
  # normal-mode splitting function measurements, Geophys. J. Int. 184,
  # 1223-1236. The scaling between the shear wave perturbation and the density
  # perturbation can be constant and set by the user with the 'Vs to density
  # scaling' parameter or depth-dependent and read in from a file. To convert
  # density the user can specify the 'Thermal expansion coefficient in initial
  # temperature scaling' parameter. The scaling is as follows: $\delta \ln
  # \rho (r,\theta,\phi) = \xi \cdot \delta \ln v_s(r,\theta, \phi)$ and
  # $\delta T(r,\theta,\phi) = - \frac{1}{\alpha} \delta \ln
  # \rho(r,\theta,\phi)$. $\xi$ is the `vs to density scaling' parameter and
  # $\alpha$ is the 'Thermal expansion coefficient in initial temperature
  # scaling' parameter. The temperature perturbation is added to an otherwise
  # constant temperature (incompressible model) or adiabatic reference profile
  # (compressible model). If a depth is specified in 'Remove temperature
  # heterogeneity down to specified depth', there is no temperature
  # perturbation prescribed down to that depth.
  # Note the required file format if the vs to density scaling is read in from
  # a file: The first lines may contain any number of comments if they begin
  # with '#', but one of these lines needs to contain the number of points in
  # the reference state as for example '# POINTS: 3'. Following the comment
  # lines there has to be a single line containing the names of all data
  # columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide the columns named `depth' and
  # `vs\_to\_density'. Note that the data lines in the file need to be sorted
  # in order of increasing depth from 0 to the maximal depth in the model
  # domain. Points in the model that are outside of the provided depth range
  # will be assigned the maximum or minimum depth values, respectively. Points
  # do not need to be equidistant, but the computation of properties is
  # optimized in speed if they are.
  # If the plugin is used in 2D it will use an equatorial slice of the seismic
  # tomography model.
  # 
  # `SAVANI perturbation': An initial temperature field in which the
  # temperature is perturbed following the SAVANI shear wave velocity model by
  # Auer and others, which can be downloaded here
  # \url{http://n.ethz.ch/~auerl/savani.tar.bz2}. Information on the vs model
  # can be found in Auer, L., Boschi, L., Becker, T.W., Nissen-Meyer, T. \&
  # Giardini, D., 2014. Savani: A variable resolution whole-mantle model of
  # anisotropic shear velocity variations based on multiple data sets. Journal
  # of Geophysical Research: Solid Earth 119.4 (2014): 3006-3034. The scaling
  # between the shear wave perturbation and the density perturbation can be
  # constant and set by the user with the 'Vs to density scaling' parameter or
  # depth-dependent and read in from a file. To convert density the user can
  # specify the 'Thermal expansion coefficient in initial temperature scaling'
  # parameter. The scaling is as follows: $\delta \ln \rho (r,\theta,\phi) =
  # \xi \cdot \delta \ln v_s(r,\theta, \phi)$ and $\delta T(r,\theta,\phi) = -
  # \frac{1}{\alpha} \delta \ln \rho(r,\theta,\phi)$. $\xi$ is the `vs to
  # density scaling' parameter and $\alpha$ is the 'Thermal expansion
  # coefficient in initial temperature scaling' parameter. The temperature
  # perturbation is added to an otherwise constant temperature (incompressible
  # model) or adiabatic reference profile (compressible model).If a depth is
  # specified in 'Remove temperature heterogeneity down to specified depth',
  # there is no temperature perturbation prescribed down to that depth.
  # Note the required file format if the vs to density scaling is read in from
  # a file: The first lines may contain any number of comments if they begin
  # with '#', but one of these lines needs to contain the number of points in
  # the reference state as for example '# POINTS: 3'. Following the comment
  # lines there has to be a single line containing the names of all data
  # columns, separated by arbitrarily many spaces. Column names are not
  # allowed to contain spaces. The file can contain unnecessary columns, but
  # for this plugin it needs to at least provide the columns named `depth' and
  # `vs\_to\_density'. Note that the data lines in the file need to be sorted
  # in order of increasing depth from 0 to the maximal depth in the model
  # domain. Points in the model that are outside of the provided depth range
  # will be assigned the maximum or minimum depth values, respectively. Points
  # do not need to be equidistant, but the computation of properties is
  # optimized in speed if they are.
  # 
  # `adiabatic': Temperature is prescribed as an adiabatic profile with upper
  # and lower thermal boundary layers, whose ages are given as input
  # parameters.
  # 
  # `adiabatic boundary': An initial temperature condition that allows for
  # discretizing the model domain into two layers separated by a user-defined
  # isothermal boundary. The user includes an input ascii data file that is
  # formatted as 3 columns of `longitude(radians)', `colatitude(radians)', and
  # `isotherm depth(meters)', where `isotherm depth' represents the depth of
  # an initial temperature of 1673.15 K (by default). The first lines in the
  # data file may contain any number of comments if they begin with `#', but
  # one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 69 121'. Note that the coordinates
  # need to be sorted in a specific order: the `longitude' coordinate needs to
  # ascend first, followed by the `colatitude' coordinate in order to assign
  # the correct data (isotherm depth) to the prescribed coordinates. The
  # temperature is defined from the surface (273.15 K) to the isotherm depth
  # (1673.15 K) as a linear gradient. Below the isotherm depth the temperature
  # increases approximately adiabatically (0.0005 K per meter). This plugin
  # should work for all geometry models, but is currently only tested for
  # spherical models.
  # 
  # `ascii data': Implementation of a model in which the initial temperature
  # is derived from files containing data in ascii format. Note the required
  # format of the input data: The first lines may contain any number of
  # comments if they begin with `#', but one of these lines needs to contain
  # the number of grid points in each dimension as for example `# POINTS: 3
  # 3'. The order of the data columns has to be `x', `y', `Temperature [K]' in
  # a 2d model and  `x', `y', `z', `Temperature [K]' in a 3d model, which
  # means that there has to be a single column containing the temperature.
  # Note that the data in the input files need to be sorted in a specific
  # order: the first coordinate needs to ascend first, followed by the second
  # and the third at last in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the radial distance of the point to
  # the bottom of the model, `y' by the azimuth angle and `z' by the polar
  # angle measured positive from the north pole. The grid will be assumed to
  # be a latitude-longitude grid. Note that the order of spherical coordinates
  # is `r', `phi', `theta' and not `r', `theta', `phi', since this allows for
  # dimension independent expressions.
  # 
  # `ascii data layered': Implementation of a model in which the initial
  # temperature is derived from files containing data in ascii format. Each
  # file defines a surface on which temperature is defined. Between the
  # surfaces, the temperatures can be chosen to be constant (with a value
  # defined by the nearest shallower surface), or linearly interpolated
  # between surfaces. Note the required format of the input ascii data file:
  # The first lines may contain any number of comments if they begin with `#',
  # but one of these lines needs to contain the number of grid points in each
  # dimension as for example `# POINTS: 3 3'. The order of the data columns
  # has to be `x', `y', `Temperature [K]' in a 2d model and `x', `y', `z',
  # `Temperature [K]' in a 3d model; i.e. the last two columns always contain
  # the position of the isotherm along the vertical direction, and the
  # temperature at that point. The first column needs to ascend first,
  # followed by the second in order to assign the correct data to the
  # prescribed coordinates. If you use a spherical model, then the assumed
  # grid changes. `x' will be replaced by the azimuth angle and `y' (if 3D) by
  # the polar angle measured positive from the north pole. The last column
  # will be the distance of the point from the origin (i.e. radial position).
  # The grid in this case will be a latitude-longitude grid. Note that the
  # order of spherical coordinates in 3D is `phi', `theta', `r', `T'and not
  # `theta', `phi', `r', `T' as this is more consistent with other ASPECT
  # plugins. Outside of the region defined by the grid, the plugin will use
  # the value at the edge of the region.
  # 
  # `ascii profile': Implementation of a model in which the initial
  # temperature is read from a file that provides these values as a function
  # of depth. Note the required format of the input data: The first lines may
  # contain any number of comments if they begin with `#', but one of these
  # lines needs to contain the number of points in the temperature profile,
  # for example `# POINTS: 10'. Following the comment lines, there has to be a
  # single line containing the names of all data columns, separated by
  # arbitrarily many spaces. Column names are not allowed to contain spaces.
  # The file can contain unnecessary columns, but for this plugin it needs to
  # at least provide columns named `depth' and`temperature'.Note that the data
  # lines in the file need to be sorted in order of increasing depth from 0 to
  # the maximal depth in the model domain. Points in the model that are
  # outside of the provided depth range will be assigned the maximum or
  # minimum depth values, respectively. Points do not need to be equidistant,
  # but the computation of properties is optimized in speed if they are.
  # 
  # `continental geotherm': This is a temperature initial condition that
  # computes a continental geotherm based on the solution of the steady-state
  # conductive equation $k\frac{d^2 T}{dy^2}+\rho H = 0$ as described in e.g.
  # Turcotte and Schubert, Ch. 4.6, or Chapman (1986). As boundary conditions,
  # we take the surface temperature and the temperature of the
  # Lithosphere-Asthenosphere Boundary (LAB).
  # The geotherm is computed for a homogeneous lithosphere composed of an
  # upper crust, lower crust and mantle layer. The crustal layers are assumed
  # to have a constant radioactive heating, and all layers are assumed to have
  # a constant thermal conductivity. Layer thicknesses, surface temperature
  # and LAB temperature should be specified by the user. For consistency, the
  # density, heat production and thermal conductivity of each layer are read
  # from the visco plastic material model and the compositional heating model.
  # 
  # For any depths below the depth of the LAB, a unrealistically high
  # temperature is returned, such that this plugin can be combined with
  # another temperature plugin through the 'minimum' operator.
  # Note that the current implementation only works for a 3-layer lithosphere,
  # even though in principle the heat conduction equation can be solved for
  # any number of layers. The naming of the compositional fields that
  # represent the layers is also very specific, namely `upper\_crust',
  # `lower\_crust', and `lithospheric\_mantle'.
  # Make sure the top and bottom temperatures of the lithosphere agree with
  # temperatures set in for example the temperature boundary conditions.
  # 
  # `function': Specify the initial temperature in terms of an explicit
  # formula. The format of these functions follows the syntax understood by
  # the muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `harmonic perturbation': An initial temperature field in which the
  # temperature is perturbed following a harmonic function (spherical harmonic
  # or sine depending on geometry and dimension) in lateral and radial
  # direction from an otherwise constant temperature (incompressible model) or
  # adiabatic reference profile (compressible model).
  # 
  # `inclusion shape perturbation': An initial temperature field in which
  # there is an inclusion in a constant-temperature box field. The size,
  # shape, gradient, position, and temperature of the inclusion are defined by
  # parameters.
  # 
  # `lithosphere mask': Implementation of a model in which the initial
  # temperature is set to a specified lithosphere temperature above the
  # lithosphere-asthenosphere boundary (specified by an ascii file or maximum
  # lithosphere depth value). Below this the initial temperature is set as
  # NaN.  Note the required format of the input data file: The first lines may
  # contain any number of comments if they begin with '#', but one of these
  # lines needs to contain the number of grid points in each dimension as for
  # example '# POINTS: 3 3'. For a spherical model, the order of the data
  # columns has to be 'phi', 'theta', 'depth (m)', where phi is the azimuth
  # angle and theta is the polar angle measured positive from the north pole.
  # This plug-in can be combined with another using the 'replace if valid'
  # operator.
  # 
  # `mandelbox': Fractal-shaped temperature field.
  # 
  # `patch on S40RTS': Implementation of a model in which the initial
  # temperature is derived from a file containing shear wave velocity
  # perturbations in ascii format (e.g. a high resolution upper mantle
  # tomography) combined with S40RTS. Note the required format of the input
  # ascii input data: The first lines may contain any number of comments if
  # they begin with '#', but one of these lines needs to contain the number of
  # grid points in each dimension as for example '# POINTS: 3 3 3'. The order
  # of the data columns has to be  `x', `y', `z', 'Vs Perturbation' in a 3d
  # model, which means that there has to be a single column containing the
  # temperature. Note that the data in the input files need to be sorted in a
  # specific order: the first coordinate needs to ascend first, followed by
  # the second and the third at last in order to assign the correct data to
  # the prescribed coordinates. In the spherical model data will be handled as
  # Cartesian, however, `x' will be replaced by the radial distance of the
  # point to the bottom of the model, `y' by the azimuth angle and `z' by the
  # polar angle measured positive from the north pole. The grid will be
  # assumed to be a latitude-longitude grid. Note that the order of spherical
  # coordinates is `r', `phi', `theta' and not `r', `theta', `phi', since this
  # allows for dimension independent expressions. See S40RTS documentation for
  # details on input parameters in the S40RTS perturbation subsection. The
  # boundary between the two tomography models is smoothed using a depth
  # weighted combination of Vs values within the region of smoothing.
  # 
  # `perturbed box': An initial temperature field in which the temperature is
  # perturbed slightly from an otherwise constant value equal to one. The
  # perturbation is chosen in such a way that the initial temperature is
  # constant to one along the entire boundary.
  # 
  # `polar box': An initial temperature field in which the temperature is
  # perturbed slightly from an otherwise constant value equal to one. The
  # perturbation is such that there are two poles on opposing corners of the
  # box.
  # 
  # `spherical gaussian perturbation': An initial temperature field in which
  # the temperature is perturbed by a single Gaussian added to an otherwise
  # spherically symmetric state. Additional parameters are read from the
  # parameter file in subsection 'Spherical gaussian perturbation'.
  # 
  # `spherical hexagonal perturbation': An initial temperature field in which
  # the temperature is perturbed following an $N$-fold pattern in a specified
  # direction from an otherwise spherically symmetric state. The class's name
  # comes from previous versions when the only option was $N=6$.
  # 
  # `world builder': Specify the initial temperature through the World
  # Builder. More information on the World Builder can be found at
  # \url{https://geodynamicworldbuilder.github.io}. Make sure to specify the
  # location of the World Builder file in the parameter 'World builder file'.
  # 
  # \textbf{Warning}: This parameter provides an old and deprecated way of
  # specifying initial temperature models and shouldn't be used. Please use
  # 'List of model names' instead.
  set Model name              = function # default: unspecified


  subsection Adiabatic
    # The age of the lower thermal boundary layer, used for the calculation of
    # the half-space cooling model temperature. Units: years if the 'Use years
    # in output instead of seconds' parameter is set; seconds otherwise.
    set Age bottom boundary layer = 0.

    # The age of the upper thermal boundary layer, used for the calculation of
    # the half-space cooling model temperature. Units: years if the 'Use years
    # in output instead of seconds' parameter is set; seconds otherwise.
    set Age top boundary layer    = 0.

    # The amplitude (in K) of the initial spherical temperature perturbation
    # at the bottom of the model domain. This perturbation will be added to
    # the adiabatic temperature profile, but not to the bottom thermal
    # boundary layer. Instead, the maximum of the perturbation and the bottom
    # boundary layer temperature will be used.
    set Amplitude                 = 0.

    # Where the initial temperature perturbation should be placed. If `center'
    # is given, then the perturbation will be centered along a `midpoint' of
    # some sort of the bottom boundary. For example, in the case of a box
    # geometry, this is the center of the bottom face; in the case of a
    # spherical shell geometry, it is along the inner surface halfway between
    # the bounding radial lines.
    set Position                  = center

    # The Radius (in m) of the initial spherical temperature perturbation at
    # the bottom of the model domain.
    set Radius                    = 0.

    # If this value is larger than 0, the initial temperature profile will not
    # be adiabatic, but subadiabatic. This value gives the maximal deviation
    # from adiabaticity. Set to 0 for an adiabatic temperature profile. Units:
    # \si{\kelvin}.
    # 
    # The function object in the Function subsection represents the
    # compositional fields that will be used as a reference profile for
    # calculating the thermal diffusivity. This function is one-dimensional
    # and depends only on depth. The format of this functions follows the
    # syntax understood by the muparser library, see
    # Section~\ref{sec:muparser-format}.
    set Subadiabaticity           = 0.


    subsection Function
      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants  = 

      # The formula that denotes the function you want to evaluate for
      # particular values of the independent variables. This expression may
      # contain any of the usual operations such as addition or
      # multiplication, as well as all of the common functions such as `sin'
      # or `cos'. In addition, it may contain expressions like `if(x>0, 1,
      # -1)' where the expression evaluates to the second argument if the
      # first argument is true, and to the third argument otherwise. For a
      # full overview of possible expressions accepted see the documentation
      # of the muparser library at http://muparser.beltoforion.de/.
      # 
      # If the function you are describing represents a vector-valued function
      # with multiple components, then separate the expressions for individual
      # components by a semicolon.
      set Function expression = 0

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names      = x,t
    end

  end

  subsection Adiabatic boundary
    # The value of the adiabatic temperature gradient. Units:
    # \si{\kelvin\per\meter}.
    set Adiabatic temperature gradient = 0.0005

    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory                 = $ASPECT_SOURCE_DIR/data/initial-temperature/adiabatic-boundary/

    # The file name of the model data.
    set Data file name                 = adiabatic_boundary.txt

    # The value of the isothermal boundary temperature. Units: \si{\kelvin}.
    set Isotherm temperature           = 1673.15

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor                   = 1.

    # The value of the surface temperature. Units: \si{\kelvin}.
    set Surface temperature            = 273.15
  end

  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory       = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/

    # The file name of the model data.
    set Data file name       = initial_isotherm_500K_box_3d.txt

    # The file names of the model data (comma separated).
    set Data file names      = initial_isotherm_500K_box_3d.txt

    # Method to interpolate between layer boundaries. Select from piecewise
    # constant or linear. Piecewise constant takes the value from the nearest
    # layer boundary above the data point. The linear option interpolates
    # linearly between layer boundaries. Above and below the domain given by
    # the layer boundaries, the values aregiven by the top and bottom layer
    # boundary.
    set Interpolation scheme = linear

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor         = 1.
  end

  subsection Ascii profile
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-profile/tests/

    # The file name of the model data.
    set Data file name = simple_test.txt

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor   = 1.
  end

  subsection Continental geotherm
    # List of the 3 thicknesses of the lithospheric layers 'upper\_crust',
    # 'lower\_crust' and 'mantle\_lithosphere'. If only one thickness is
    # given, then the same thickness is used for all layers. Units:
    # \si{meter}.
    set Layer thicknesses                           = 30000.

    # The value of the isotherm that is assumed at the
    # Lithosphere-Asthenosphere boundary. Units: \si{\kelvin}.
    set Lithosphere-Asthenosphere boundary isotherm = 1673.15

    # The value of the surface temperature. Units: \si{\kelvin}.
    set Surface temperature                         = 273.15
  end

  subsection Function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `cartesian', `spherical', and
    # `depth'. `spherical' coordinates are interpreted as r,phi or r,phi,theta
    # in 2D/3D respectively with theta being the polar angle. `depth' will
    # create a function, in which only the first parameter is non-zero, which
    # is interpreted to be the depth of the point.
    set Coordinate system   = cartesian

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = H=6.0e5, Hl=5.0e4, TS=273.0, T0=1573.0, kappa=0.7272e-6, t50=1.5778463e15                                            # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = if(x<=(H-y),TS+(T0-TS)*(1.0-erfc( (H-y)/(2.0*sqrt(kappa*t50))) ), if(x>(H-y) & y>(H-Hl), TS+(T0-TS)*(H-y)/Hl, T0 ) ) # default: 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Harmonic perturbation
    # Doubled first lateral wave number of the harmonic perturbation. Equals
    # the spherical harmonic degree in 3D spherical shells. In all other cases
    # one equals half of a sine period over the model domain. This allows for
    # single up-/downswings. Negative numbers reverse the sign of the
    # perturbation but are not allowed for the spherical harmonic case.
    set Lateral wave number one = 3

    # Doubled second lateral wave number of the harmonic perturbation. Equals
    # the spherical harmonic order in 3D spherical shells. In all other cases
    # one equals half of a sine period over the model domain. This allows for
    # single up-/downswings. Negative numbers reverse the sign of the
    # perturbation.
    set Lateral wave number two = 2

    # The magnitude of the Harmonic perturbation.
    set Magnitude               = 1.0

    # The reference temperature that is perturbed by the harmonic function.
    # Only used in incompressible models.
    set Reference temperature   = 1600.0

    # Doubled radial wave number of the harmonic perturbation.  One equals
    # half of a sine period over the model domain.  This allows for single
    # up-/downswings. Negative numbers  reverse the sign of the perturbation.
    set Vertical wave number    = 1
  end

  subsection Inclusion shape perturbation
    # The background temperature for the temperature field.
    set Ambient temperature   = 1.0

    # The X coordinate for the center of the shape.
    set Center X              = 0.5

    # The Y coordinate for the center of the shape.
    set Center Y              = 0.5

    # The Z coordinate for the center of the shape. This is only necessary for
    # three-dimensional fields.
    set Center Z              = 0.5

    # The gradient of the inclusion to be generated.
    set Inclusion gradient    = constant

    # The shape of the inclusion to be generated.
    set Inclusion shape       = circle

    # The temperature of the inclusion shape. This is only the true
    # temperature in the case of the constant gradient. In all other cases, it
    # gives one endpoint of the temperature gradient for the shape.
    set Inclusion temperature = 0.0

    # The radius of the inclusion to be generated. For shapes with no radius
    # (e.g. square), this will be the width, and for shapes with no width,
    # this gives a general guideline for the size of the shape.
    set Shape radius          = 1.0
  end

  subsection Lithosphere Mask
    # The path to the LAB depth data file
    set Data directory             = $ASPECT_SOURCE_DIR/data/initial-temperature/lithosphere-mask/

    # Method that is used to specify the depth of the
    # lithosphere-asthenosphere boundary.
    set Depth specification method = Value

    # File from which the lithosphere-asthenosphere boundary depth data is
    # read.
    set LAB depth filename         = LAB_CAM2016.txt

    # The initial temperature within lithosphere, applied abovethe maximum
    # lithosphere depth.
    set Lithosphere temperature    = 1600.

    # Units: \si{\meter}.The maximum depth of the lithosphere. The model will
    # be NaNs below this depth.
    set Maximum lithosphere depth  = 200000.0
  end

  subsection Patch on S40RTS
    # The maximum depth of the Vs ascii grid. The model will read in  Vs from
    # S40RTS below this depth.
    set Maximum grid depth                                       = 700000.0

    # This will set the heterogeneity prescribed by the Vs ascii grid and
    # S40RTS to zero down to the specified depth (in meters). Note that your
    # resolution has to be adequate to capture this cutoff. For example if you
    # specify a depth of 660km, but your closest spherical depth layers are
    # only at 500km and 750km (due to a coarse resolution) it will only zero
    # out heterogeneities down to 500km. Similar caution has to be taken when
    # using adaptive meshing.
    set Remove temperature heterogeneity down to specified depth = -1.7976931348623157e+308

    # The depth range (above maximum grid depth) over which to smooth. The
    # boundary is smoothed using a depth weighted combination of Vs values
    # from the ascii grid and S40RTS at each point in the region of
    # smoothing.
    set Smoothing length scale                                   = 200000.0


    subsection Ascii data model
      # The name of a directory that contains the model data. This path may
      # either be absolute (if starting with a `/') or relative to the current
      # directory. The path may also include the special text
      # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
      # the ASPECT source files were located when ASPECT was compiled. This
      # interpretation allows, for example, to reference files located in the
      # `data/' subdirectory of ASPECT.
      set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/patch-on-S40RTS/test/

      # The file name of the model data.
      set Data file name = upper_shell_3d.txt

      # Scalar factor, which is applied to the model data. You might want to
      # use this to scale the input to a reference model. Another way to use
      # this factor is to convert units of the input files. For instance, if
      # you provide velocities in cm/yr set this factor to 0.01.
      set Scale factor   = 1.
    end

  end

  subsection S40RTS perturbation
    # The path to the model data.
    set Data directory                                               = $ASPECT_SOURCE_DIR/data/initial-temperature/S40RTS/

    # The file name of the spherical harmonics coefficients from Ritsema et
    # al.
    set Initial condition file name                                  = S40RTS.sph

    # The maximum order the users specify when reading the data file of
    # spherical harmonic coefficients, which must be smaller than the maximum
    # order the data file stored. This parameter will be used only if 'Specify
    # a lower maximum order' is set to true.
    set Maximum order                                                = 20

    # The reference temperature that is perturbed by the spherical harmonic
    # functions. Only used in incompressible models.
    set Reference temperature                                        = 1600.0

    # Option to remove the degree zero component from the perturbation, which
    # will ensure that the laterally averaged temperature for a fixed depth is
    # equal to the background temperature.
    set Remove degree 0 from perturbation                            = true

    # This will set the heterogeneity prescribed by S20RTS or S40RTS to zero
    # down to the specified depth (in meters). Note that your resolution has
    # to be adequate to capture this cutoff. For example if you specify a
    # depth of 660km, but your closest spherical depth layers are only at
    # 500km and 750km (due to a coarse resolution) it will only zero out
    # heterogeneities down to 500km. Similar caution has to be taken when
    # using adaptive meshing.
    set Remove temperature heterogeneity down to specified depth     = -1.7976931348623157e+308

    # Option to use a lower maximum order when reading the data file of
    # spherical harmonic coefficients. This is probably used for the faster
    # tests or when the users only want to see the spherical harmonic pattern
    # up to a certain order.
    set Specify a lower maximum order                                = false

    # The file name of the spline knot locations from Ritsema et al.
    set Spline knots depth file name                                 = Spline_knots.txt

    # The value of the thermal expansion coefficient $\beta$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient in initial temperature scaling = 2e-5

    # Option to take the thermal expansion coefficient from the material model
    # instead of from what is specified in this section.
    set Use thermal expansion coefficient from material model        = false

    # This parameter specifies how the perturbation in shear wave velocity as
    # prescribed by S20RTS or S40RTS is scaled into a density perturbation.
    # See the general description of this model for more detailed
    # information.
    set Vs to density scaling                                        = 0.25

    # Method that is used to specify how the vs-to-density scaling varies with
    # depth.
    set Vs to density scaling method                                 = constant


    subsection Ascii data vs to density model
      # The name of a directory that contains the model data. This path may
      # either be absolute (if starting with a `/') or relative to the current
      # directory. The path may also include the special text
      # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
      # the ASPECT source files were located when ASPECT was compiled. This
      # interpretation allows, for example, to reference files located in the
      # `data/' subdirectory of ASPECT.
      set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/S40RTS/

      # The file name of the model data.
      set Data file name = vs_to_density_Steinberger.txt

      # Scalar factor, which is applied to the model data. You might want to
      # use this to scale the input to a reference model. Another way to use
      # this factor is to convert units of the input files. For instance, if
      # you provide velocities in cm/yr set this factor to 0.01.
      set Scale factor   = 1.
    end

  end

  subsection SAVANI perturbation
    # The path to the model data.
    set Data directory                                               = $ASPECT_SOURCE_DIR/data/initial-temperature/SAVANI/

    # The file name of the spherical harmonics coefficients from Auer et al.
    set Initial condition file name                                  = savani.dlnvs.60.m.ab

    # The maximum order the users specify when reading the data file of
    # spherical harmonic coefficients, which must be smaller than the maximum
    # order the data file stored. This parameter will be used only if 'Specify
    # a lower maximum order' is set to true.
    set Maximum order                                                = 20

    # The reference temperature that is perturbed by the spherical harmonic
    # functions. Only used in incompressible models.
    set Reference temperature                                        = 1600.0

    # Option to remove the degree zero component from the perturbation, which
    # will ensure that the laterally averaged temperature for a fixed depth is
    # equal to the background temperature.
    set Remove degree 0 from perturbation                            = true

    # This will set the heterogeneity prescribed by SAVANI to zero down to the
    # specified depth (in meters). Note that your resolution has to be
    # adequate to capture this cutoff. For example if you specify a depth of
    # 660km, but your closest spherical depth layers are only at 500km and
    # 750km (due to a coarse resolution) it will only zero out heterogeneities
    # down to 500km. Similar caution has to be taken when using adaptive
    # meshing.
    set Remove temperature heterogeneity down to specified depth     = -1.7976931348623157e+308

    # Option to use a lower maximum order when reading the data file of
    # spherical harmonic coefficients. This is probably used for the faster
    # tests or when the users only want to see the spherical harmonic pattern
    # up to a certain order.
    set Specify a lower maximum order                                = false

    # The file name of the spline knots taken from the 28 spherical layers of
    # SAVANI tomography model.
    set Spline knots depth file name                                 = Spline_knots.txt

    # The value of the thermal expansion coefficient $\beta$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient in initial temperature scaling = 2e-5

    # Option to take the thermal expansion coefficient from the material model
    # instead of from what is specified in this section.
    set Use thermal expansion coefficient from material model        = false

    # This parameter specifies how the perturbation in shear wave velocity as
    # prescribed by SAVANI is scaled into a density perturbation. See the
    # general description of this model for more detailed information.
    set Vs to density scaling                                        = 0.25

    # Method that is used to specify how the vs-to-density scaling varies with
    # depth.
    set Vs to density scaling method                                 = constant


    subsection Ascii data vs to density model
      # The name of a directory that contains the model data. This path may
      # either be absolute (if starting with a `/') or relative to the current
      # directory. The path may also include the special text
      # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
      # the ASPECT source files were located when ASPECT was compiled. This
      # interpretation allows, for example, to reference files located in the
      # `data/' subdirectory of ASPECT.
      set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/S40RTS/

      # The file name of the model data.
      set Data file name = vs_to_density_Steinberger.txt

      # Scalar factor, which is applied to the model data. You might want to
      # use this to scale the input to a reference model. Another way to use
      # this factor is to convert units of the input files. For instance, if
      # you provide velocities in cm/yr set this factor to 0.01.
      set Scale factor   = 1.
    end

  end

  subsection Spherical gaussian perturbation
    # The amplitude of the perturbation.
    set Amplitude                           = 0.01

    # The angle where the center of the perturbation is placed.
    set Angle                               = 0.

    # The file from which the initial geotherm table is to be read. The format
    # of the file is defined by what is read in
    # source/initial\_conditions/spherical\_shell.cc.
    set Filename for initial geotherm table = initial-geotherm-table

    # The non-dimensional radial distance where the center of the perturbation
    # is placed.
    set Non-dimensional depth               = 0.7

    # The standard deviation of the Gaussian perturbation.
    set Sigma                               = 0.2

    # The sign of the perturbation.
    set Sign                                = 1.
  end

  subsection Spherical hexagonal perturbation
    # The number of convection cells with which to perturb the system.
    set Angular mode    = 6

    # Amount of clockwise rotation in degrees to apply to the perturbations.
    # Default is set to -45 in order to provide backwards compatibility.
    set Rotation offset = -45.
  end

end


subsection Material model
  # Whether or not (and in the first case, how) to do any averaging of
  # material model output data when constructing the linear systems for
  # velocity/pressure, temperature, and compositions in each time step, as
  # well as their corresponding preconditioners.
  # 
  # Possible choices: none|arithmetic average|harmonic average|geometric
  # average|pick largest|project to Q1|log average|harmonic average only
  # viscosity|project to Q1 only viscosity
  # 
  # The process of averaging, and where it may be used, is discussed in more
  # detail in Section~\ref{sec:sinker-with-averaging}.
  # 
  # More averaging schemes are available in the averaging material model. This
  # material model is a ``compositing material model'' which can be used in
  # combination with other material models.
  set Material averaging = none

  # The name of the material model to be used in this simulation. There are
  # many material models you can choose from, as listed below. They generally
  # fall into two category: (i) models that implement a particular case of
  # material behavior, (ii) models that modify other models in some way. We
  # sometimes call the latter ``compositing models''. An example of a
  # compositing model is the ``depth dependent'' model below in that it takes
  # another, freely choosable model as its base and then modifies that model's
  # output in some way.
  # 
  # You can select one of the following models:
  # 
  # `Steinberger': This material model looks up the viscosity from the tables
  # that correspond to the paper of Steinberger and Calderwood 2006 (``Models
  # of large-scale viscous flow in the Earth's mantle with constraints from
  # mineral physics and surface observations'', Geophys. J. Int., 167,
  # 1461-1481, \url{http://dx.doi.org/10.1111/j.1365-246X.2006.03131.x}) and
  # material data from a database generated by the thermodynamics code
  # \texttt{Perplex}, see \url{http://www.perplex.ethz.ch/}. The default
  # example data builds upon the thermodynamic database by Stixrude 2011 and
  # assumes a pyrolitic composition by Ringwood 1988 but is easily replaceable
  # by other data files.
  # 
  # `ascii reference profile': A material model that reads in a reference
  # state for density, thermal expansivity, compressibility and specific heat
  # from a text file.
  # Note the required format of the input data: The first lines may contain
  # any number of comments if they begin with `#', but one of these lines
  # needs to contain the number of points in the reference state as for
  # example `# POINTS: 3'. Following the comment lines there has to be a
  # single line containing the names of all data columns, separated by
  # arbitrarily many spaces. Column names are not allowed to contain spaces.
  # The file can contain unnecessary columns, but for this plugin it needs to
  # at least provide the columns named `density', `thermal\_expansivity',
  # `specific\_heat', and `compressibility'. Note that the data lines in the
  # file need to be sorted in order of increasing depth from 0 to the maximal
  # depth in the model domain. Points in the model that are outside of the
  # provided depth range will be assigned the maximum or minimum depth values,
  # respectively. Points do not need to be equidistant, but the computation of
  # properties is optimized in speed if they are.
  # 
  # The viscosity $\eta$ is computed as \begin{equation}\eta(z,T) = \eta_r(z)
  # \eta_0 \exp\left(-A \frac{T -
  # T_{\text{adi}}}{T_{\text{adi}}}\right),\end{equation}where $\eta_r(z)$ is
  # the depth-dependence, which is a piecewise constant function computed
  # according to the list of ``Viscosity prefactors'' and ``Transition
  # depths'', $\eta_0$ is the reference viscosity specified by the parameter
  # ``Viscosity'' and $A$ describes the dependence on temperature and
  # corresponds to the parameter ``Thermal viscosity exponent''.
  # 
  # `averaging': The ``averaging'' Material model applies an averaging of the
  # quadrature points within a cell. The values to average are supplied by any
  # of the other available material models. In other words, it is a
  # ``compositing material model''. Parameters related to the average model
  # are read from a subsection ``Material model/Averaging''.
  # 
  # The user must specify a ``Base model'' from which material properties are
  # derived. Furthermore an averaging operation must be selected, where the
  # Choice should be from the list none|arithmetic average|harmonic
  # average|geometric average|pick largest|log average|NWD arithmetic
  # average|NWD harmonic average|NWD geometric average.
  # 
  # NWD stands for Normalized Weighed Distance. The models with this in front
  # of their name work with a weighed average, which means each quadrature
  # point requires an individual weight. The weight is determined by the
  # distance, where the exact relation is determined by a bell shaped curve. A
  # bell shaped curve is a continuous function which is one at its maximum and
  # exactly zero at and beyond its limit. This bell shaped curve is spanned
  # around each quadrature point to determine the weighting map for each
  # quadrature point. The used bell shape comes from Lucy (1977). The distance
  # is normalized so the largest distance becomes one. This means that if
  # variable ''Bell shape limit'' is exactly one, the farthest quadrature
  # point is just on the limit and its weight will be exactly zero. In this
  # plugin it is not implemented as larger and equal than the limit, but
  # larger than, to ensure the quadrature point at distance zero is always
  # included.
  # 
  # `compositing': The ``compositing'' Material model selects material model
  # properties from a given set of other material models, and is intended to
  # make mixing different material models easier.
  # 
  # Specifically, this material model works by allowing to specify the name of
  # another material model for each coefficient that material models are asked
  # for (such as the viscosity, density, etc.). Whenever the material model is
  # asked for the values of coefficients, it then evaluates all of the ``base
  # models'' that were listed for the various coefficients, and copies the
  # values returned by these base models into the output structure.
  # 
  # The implementation of this material model is somewhat expensive because it
  # has to evaluate all material coefficients of all underlying material
  # models. Consequently, if performance of assembly and postprocessing is
  # important, then implementing a separate material model is a better choice
  # than using this material model.
  # 
  # `composition reaction': A material model that behaves in the same way as
  # the simple material model, but includes two compositional fields and a
  # reaction between them. Above a depth given in the input file, the first
  # fields gets converted to the second field.
  # 
  # `depth dependent': The ``depth dependent'' Material model applies a
  # depth-dependent scaling to any of the other available material models. In
  # other words, it is a ``compositing material model''.
  # 
  # Parameters related to the depth dependent model are read from a subsection
  # ``Material model/Depth dependent model''. The user must specify a ``Base
  # model'' from which material properties are derived. Currently the depth
  # dependent model only allows depth dependence of viscosity - other material
  # properties are taken from the ``Base model''. Viscosity $\eta$ at depth
  # $z$ is calculated according to:\begin{equation}\eta(z,p,T,X,...) = \eta(z)
  # \eta_b(p,T,X,..)/\eta_{rb}\end{equation}where $\eta(z)$ is the
  # depth-dependence specified by the depth dependent model,
  # $\eta_b(p,T,X,...)$ is the viscosity calculated from the base model, and
  # $\eta_{rb}$ is the reference viscosity of the ``Base model''. In addition
  # to the specification of the ``Base model'', the user must specify the
  # method to be used to calculate the depth-dependent viscosity $\eta(z)$ as
  # ``Material model/Depth dependent model/Depth dependence method'', which
  # can be chosen among ``None|Function|File|List''. Each method and the
  # associated parameters are as follows:
  # 
  # ``Function'': read a user-specified parsed function from the input file in
  # a subsection ``Material model/Depth dependent model/Viscosity depth
  # function''. By default, this function is uniformly equal to 1.0e21.
  # Specifying a function that returns a value less than or equal to 0.0
  # anywhere in the model domain will produce an error.
  # 
  # ``File'': read a user-specified file containing viscosity values at
  # specified depths. The file containing depth-dependent viscosities is read
  # from a directory specified by the user as ``Material model/Depth dependent
  # model/Data directory'', from a file with name specified as ``Material
  # model/Depth dependent model/Viscosity depth file''. The format of this
  # file is ascii text and contains two columns with one header line:
  # 
  # example Viscosity depth file:\\Depth (m)    Viscosity
  # (Pa-s)\\0.0000000e+00     1.0000000e+21\\6.7000000e+05     1.0000000e+22\\
  # 
  # Viscosity is interpolated from this file using linear interpolation.
  # ``None'': no depth-dependence. Viscosity is taken directly from ``Base
  # model''
  # 
  # ``List:'': read a comma-separated list of depth values corresponding to
  # the maximum depths of layers having constant depth-dependence $\eta(z)$.
  # The layers must be specified in order of increasing depth, and the last
  # layer in the list must have a depth greater than or equal to the maximal
  # depth of the model. The list of layer depths is specified as ``Material
  # model/Depth dependent model/Depth list'' and the corresponding list of
  # layer viscosities is specified as ``Material model/Depth dependent
  # model/Viscosity list''
  # 
  # `diffusion dislocation': An implementation of a viscous rheology including
  # diffusion and dislocation creep. Compositional fields can each be assigned
  # individual activation energies, reference densities, thermal
  # expansivities, and stress exponents. The effective viscosity is defined as
  # 
  # 
  # \[\eta_{\text{eff}} = \left(\frac{1}{\eta_{\text{eff}}^\text{diff}}+
  # \frac{1}{\eta_{\text{eff}}^\text{dis}}\right)^{-1}\] where
  # \[\eta_{\text{i}} = \frac{1}{2} A^{-\frac{1}{n_i}} d^\frac{m_i}{n_i}
  # \dot{\varepsilon_i}^{\frac{1-n_i}{n_i}} \exp\left(\frac{E_i^\ast +
  # PV_i^\ast}{n_iRT}\right)\]
  # 
  # where $d$ is grain size, $i$ corresponds to diffusion or dislocation
  # creep, $\dot{\varepsilon}$ is the square root of the second invariant of
  # the strain rate tensor, $R$ is the gas constant, $T$ is temperature, and
  # $P$ is pressure. $A_i$ are prefactors, $n_i$ and $m_i$ are stress and
  # grain size exponents $E_i$ are the activation energies and $V_i$ are the
  # activation volumes.
  # 
  # This form of the viscosity equation is commonly used in geodynamic
  # simulations See, for example, Billen and Hirth (2007), G3, 8, Q08012.
  # Significantly, other studies may use slightly different forms of the
  # viscosity equation leading to variations in how specific terms are defined
  # or combined. For example, the grain size exponent should always be
  # positive in the diffusion viscosity equation used here, while other
  # studies place the grain size term in the denominator and invert the sign
  # of the grain size exponent. When examining previous work, one should
  # carefully check how the viscous prefactor and grain size terms are
  # defined.
  # 
  # The ratio of diffusion to dislocation strain rate is found by Newton's
  # method, iterating to find the stress which satisfies the above equations.
  # The value for the components of this formula and additional parameters are
  # read from the parameter file in subsection 'Material
  # model/DiffusionDislocation'.
  # 
  # `drucker prager': A material model that has constant values for all
  # coefficients but the density and viscosity. The defaults for all
  # coefficients are chosen to be similar to what is believed to be correct
  # for Earth's mantle. All of the values that define this model are read from
  # a section ``Material model/Drucker Prager'' in the input file, see
  # Section~\ref{parameters:Material_20model/Drucker_20Prager}. Note that the
  # model does not take into account any dependencies of material properties
  # on compositional fields.
  # 
  # The viscosity is computed according to the Drucker Prager frictional
  # plasticity criterion (non-associative) based on a user-defined internal
  # friction angle $\phi$ and cohesion $C$. In 3D:  $\sigma_y = \frac{6 C
  # \cos(\phi)}{\sqrt(3) (3+\sin(\phi))} + \frac{2 P \sin(\phi)}{\sqrt(3)
  # (3+\sin(\phi))}$, where $P$ is the pressure. See for example Zienkiewicz,
  # O. C., Humpheson, C. and Lewis, R. W. (1975), G\'{e}otechnique 25, No. 4,
  # 671-689. With this formulation we circumscribe instead of inscribe the
  # Mohr Coulomb yield surface. In 2D the Drucker Prager yield surface is the
  # same as the Mohr Coulomb surface:  $\sigma_y = P \sin(\phi) + C
  # \cos(\phi)$. Note that in 2D for $\phi=0$, these criteria revert to the
  # von Mises criterion (no pressure dependence). See for example Thieulot, C.
  # (2011), PEPI 188, 47-68.
  # 
  # Note that we enforce the pressure to be positive to prevent negative yield
  # strengths and viscosities.
  # 
  # We then use the computed yield strength to scale back the viscosity on to
  # the yield surface using the Viscosity Rescaling Method described in
  # Kachanov, L. M. (2004), Fundamentals of the Theory of Plasticity, Dover
  # Publications, Inc. (Not Radial Return.)A similar implementation can be
  # found in GALE (https://geodynamics.org/cig/software/gale/gale-manual.pdf).
  # 
  # 
  # To avoid numerically unfavourably large (or even negative) viscosity
  # ranges, we cut off the viscosity with a user-defined minimum and maximum
  # viscosity: $\eta_eff = \frac{1}{\frac{1}{\eta_min + \eta}+
  # \frac{1}{\eta_max}}$.
  # 
  # Note that this model uses the formulation that assumes an incompressible
  # medium despite the fact that the density follows the law
  # $\rho(T)=\rho_0(1-\beta(T-T_{\text{ref}}))$.
  # 
  # `dynamic friction': This model is for use with an arbitrary number of
  # compositional fields, where each field represents a rock type which can
  # have completely different properties from the others.Each rock type itself
  # has constant material properties, with the exception of viscosity which is
  # modified according to a Drucker-Prager yield criterion. Unlike the drucker
  # prager or visco plastic material models, the angle of internal friction is
  # a function of velocity. This relationship is similar to rate-and-state
  # friction constitutive relationships, which are applicable to the strength
  # of rocks during earthquakes. The formulation used here is derived from van
  # Dinther et al. 2013, JGR. Each compositional field is interpreed as a
  # volume fraction. If the sum of the fields is greater than one, they are
  # renormalized. If it is less than one, material properties for ``background
  # material'' make up the rest. When more than one field is present, the
  # material properties are averaged arithmetically. An exception is the
  # viscosity, where the averaging should make more of a difference. For this,
  # the user selectsbetween arithmetic, harmonic, geometric, or maximum
  # composition averaging.
  # 
  # `grain size': A material model that relies on compositional fields that
  # correspond to the average grain sizes of a mineral phase and source terms
  # that determine the grain size evolution in terms of the strain rate,
  # temperature, phase transitions, and the creep regime. This material model
  # only works if a compositional field named 'grain_size' is present. In the
  # diffusion creep regime, the viscosity depends on this grain size field. We
  # use the grain size evolution laws described in Behn et al., 2009.
  # Implications of grain size evolution on the seismic structure of the
  # oceanic upper mantle, Earth Planet. Sci. Letters, 282, 178–189. Other
  # material parameters are either prescribed similar to the 'simple' material
  # model, or read from data files that were generated by the Perplex or
  # Hefesto software. This material model is described in more detail in
  # Dannberg, J., Z. Eilon, U. Faul, R. Gassmoeller, P. Moulik, and R. Myhill
  # (2017), The importance of grain size to mantle dynamics and seismological
  # observations, Geochem. Geophys. Geosyst., 18, 3034–3061,
  # doi:10.1002/2017GC006944.
  # 
  # `latent heat': A material model that includes phase transitions and the
  # possibility that latent heat is released or absorbed when material crosses
  # one of the phase transitions of up to two different materials
  # (compositional fields). This model implements a standard approximation of
  # the latent heat terms following Christensen \& Yuen, 1985. The change of
  # entropy is calculated as $Delta S = \gamma \frac{\Delta\rho}{\rho^2}$ with
  # the Clapeyron slope $\gamma$ and the density change $\Delta\rho$ of the
  # phase transition being input parameters. The model employs an analytic
  # phase function in the form $X=\frac{1}{2} \left( 1 + \tanh \left(
  # \frac{\Delta p}{\Delta p_0} \right) \right)$ with $\Delta p = p -
  # p_{\text{transition}} - \gamma \left( T - T_{\text{transition}} \right)$
  # and $\Delta p_0$ being the pressure difference over the width of the phase
  # transition (specified as input parameter).
  # 
  # `latent heat melt': A material model that includes the latent heat of
  # melting for two materials: peridotite and pyroxenite. The melting model
  # for peridotite is taken from Katz et al., 2003 (A new parameterization of
  # hydrous mantle melting) and the one for pyroxenite from Sobolev et al.,
  # 2011 (Linking mantle plumes, large igneous provinces and environmental
  # catastrophes). The model assumes a constant entropy change for melting
  # 100\% of the material, which can be specified in the input file. The
  # partial derivatives of entropy with respect to temperature and pressure
  # required for calculating the latent heat consumption are then calculated
  # as product of this constant entropy change, and the respective derivative
  # of the function the describes the melt fraction. This is linearly averaged
  # with respect to the fractions of the two materials present. If no
  # compositional fields are specified in the input file, the model assumes
  # that the material is peridotite. If compositional fields are specified,
  # the model assumes that the first compositional field is the fraction of
  # pyroxenite and the rest of the material is peridotite.
  # 
  # Otherwise, this material model has a temperature- and pressure-dependent
  # density and viscosity and the density and thermal expansivity depend on
  # the melt fraction present. It is possible to extent this model to include
  # a melt fraction dependence of all the material parameters by calling the
  # function melt_fraction in the calculation of the respective parameter.
  # However, melt and solid move with the same velocity and melt extraction is
  # not taken into account (batch melting).
  # 
  # `melt global': A material model that implements a simple formulation of
  # the material parameters required for the modelling of melt transport,
  # including a source term for the porosity according to a simplified linear
  # melting model similar to \cite{schmeling2006}:
  # $\phi_{\text{equilibrium}} =
  # \frac{T-T_{\text{sol}}}{T_{\text{liq}}-T_{\text{sol}}}$
  # with $T_{\text{sol}} = T_{\text{sol,0}} + \Delta T_p \, p + \Delta T_c \,
  # C$
  # $T_{\text{liq}} = T_{\text{sol}}  + \Delta T_{\text{sol-liq}}$.
  # 
  # `melt simple': A material model that implements a simple formulation of
  # the material parameters required for the modelling of melt transport,
  # including a source term for the porosity according to the melting model
  # for dry peridotite of \cite{KSL2003}. This also includes a computation of
  # the latent heat of melting (if the `latent heat' heating model is active).
  # 
  # Most of the material properties are constant, except for the shear,
  # viscosity $\eta$, the compaction viscosity $\xi$, and the permeability
  # $k$, which depend on the porosity; and the solid and melt densities, which
  # depend on temperature and pressure:
  # $\eta(\phi,T) = \eta_0 e^{\alpha(\phi-\phi_0)} e^{-\beta(T-T_0)/T_0}$,
  # $\xi(\phi,T) = \xi_0 \frac{\phi_0}{\phi} e^{-\beta(T-T_0)/T_0}$, $k=k_0
  # \phi^n (1-\phi)^m$, $\rho=\rho_0 (1 - \alpha (T - T_{\text{adi}}))
  # e^{\kappa p}$.
  # 
  # The model is compressible only if this is specified in the input file, and
  # contains compressibility for both solid and melt.
  # 
  # `modified tait': A material model that implements the thermal modified
  # Tait equation of state as written in \cite{HP2011}. Constant values are
  # used for the thermal conductivity and viscosity. The defaults for all
  # coefficients are chosen to be similar to what is believed to be correct
  # for Earth's mantle. All of the values that define this model are read from
  # a section ``Material model/Modified Tait model'' in the input file, see
  # Section~\ref{parameters:Material_20model/Modified_20Tait_20model}.
  # 
  # `multicomponent': This incompressible model is for use with an arbitrary
  # number of compositional fields, where each field represents a rock type
  # which can have completely different properties from the others. However,
  # each rock type itself has constant material properties.  The value of the
  # compositional field is interpreted as a volume fraction. If the sum of the
  # fields is greater than one, they are renormalized.  If it is less than
  # one, material properties  for ``background mantle'' make up the rest. When
  # more than one field is present, the material properties are averaged
  # arithmetically.  An exception is the viscosity, where the averaging should
  # make more of a difference.  For this, the user selects between arithmetic,
  # harmonic, geometric, or maximum composition averaging.
  # 
  # `multicomponent compressible': This model is for use with an arbitrary
  # number of compositional fields, where each field represents a rock type
  # which can have completely different properties from the others. Each rock
  # type is described by a self-consistent equation of state.  The value of
  # the  compositional field is interpreted as a mass fraction. If the sum of
  # the fields is greater than one, they are renormalized.  If it is less than
  # one, material properties  for ``background mantle'' make up the rest. When
  # more than one field is present, the material properties are averaged
  # arithmetically by mass fraction (for specific heat), or volume fraction
  # (for density, thermal expansivity and compressibility). The thermal
  # conductivity is also arithmetically averaged by volume fraction. Finally,
  # the viscosity is averaged by volume fraction, but the user can choose
  # between arithmetic, harmonic, geometric or maximum composition averaging.
  # 
  # `nondimensional': A material model for nondimensionalized computations for
  # compressible or incompressible computations defined through Rayleigh
  # number 	ext{Ra} and Dissipation number Di. This model is made to be used
  # with the Boussinesq, ALA, or TALA formulation.
  # 
  # The viscosity is defined as \[\eta = \text{Di} / \text{Ra} \cdot \exp(-b
  # T' + c z)\] where $T'$ is the temperature variation from the adiabatic
  # temperature, $z$ is the depth, $b$ is given by ``Viscosity temperature
  # prefactor'', and $c$ by ``Viscosity depth prefactor''. If $\text{Di}$ is
  # zero, it will be replaced by 1.0 in $\eta$.
  # 
  # The density is defined as \[\rho = \exp(\text{Di}/\gamma \cdot z)  (1.0 -
  # \alpha T' + \text{Di} \gamma p'),\] where $\alpha=\text{Di}$ is the
  # thermal expansion coefficient, $\gamma$ is the Grueneisen parameter, and
  # $p'$ is the pressure variation from the adiabatic pressure. The pressure
  # dependent term is not present if ``TALA'' is enabled.
  # 
  # `perplex lookup': A material model that has constant values for viscosity
  # and thermal conductivity, and calculates other properties on-the-fly using
  # PerpleX meemum. Compositional fields correspond to the individual
  # components in the order given in the PerpleX file.
  # 
  # `replace lithosphere viscosity': The ``replace lithosphere viscosity''
  # Material model sets viscosity to a prescribed constant above the
  # lithosphere-asthenosphere boundary (specified by an ascii file or maximum
  # lithosphere depth). Below the lithosphere-asthenosphereboundary the
  # viscosity is taken from any of the other available material model. In
  # other words, it is a ``compositing material model''.
  # Parameters related to the replace lithosphere viscosity model are read
  # from a subsection ``Material model/Replace lithosphere viscosity''. The
  # user must specify a ``Base model'' from which other material properties
  # are derived.
  # Note the required format of the input data file: The first lines may
  # contain any number of comments if they begin with ‘#’, but one of
  # these lines needs to contain the number of grid points in each dimension
  # as for example‘# POINTS: 3 3’. For a spherical model, the order of the
  # data columns has to be'phi', 'theta','depth (m)', where phi is the
  # azimuth angle and theta is the polar angle measured positive from the
  # north pole.
  # 
  # `simple': A material model that has constant values for all coefficients
  # but the density and viscosity. The defaults for all coefficients are
  # chosen to be similar to what is believed to be correct for Earth's mantle.
  # All of the values that define this model are read from a section
  # ``Material model/Simple model'' in the input file, see
  # Section~\ref{parameters:Material_20model/Simple_20model}.
  # 
  # This model uses the following set of equations for the two coefficients
  # that are non-constant: \begin{align}  \eta(p,T,\mathfrak c) &= \tau(T)
  # \zeta(\mathfrak c) \eta_0, \\  \rho(p,T,\mathfrak c) &= \left(1-\alpha
  # (T-T_0)\right)\rho_0 + \Delta\rho \; c_0,\end{align}where $c_0$ is the
  # first component of the compositional vector $\mathfrak c$ if the model
  # uses compositional fields, or zero otherwise.
  # 
  # The temperature pre-factor for the viscosity formula above is defined as
  # \begin{align}  \tau(T) &= H\left(e^{-\beta
  # (T-T_0)/T_0}\right),\intertext{with}   \qquad\qquad H(x) &= \begin{cases}
  # \tau_{\text{min}} & \text{if}\; x<\tau_{\text{min}}, \\
  # x & \text{if}\; 10^{-2}\le x \le 10^2, \\
  # \tau_{\text{max}} & \text{if}\; x>\tau_{\text{max}}, \\
  # \end{cases}\end{align} where $x=e^{-\beta (T-T_0)/T_0}$, $\beta$
  # corresponds to the input parameter ``Thermal viscosity exponent'', and
  # $T_0$ to the parameter ``Reference temperature''. If you set $T_0=0$ in
  # the input file, the thermal pre-factor $\tau(T)=1$. The parameters
  # $\tau_{\text{min}}$ and $\tau_{\text{max}}$ set the minimum and maximum
  # values of the temperature pre-factor and are set using ``Maximum thermal
  # prefactor'' and ``Minimum thermal prefactor''. Specifying a value of 0.0
  # for the minimum or maximum values will disable pre-factor limiting.
  # 
  # The compositional pre-factor for the viscosity is defined as \begin{align}
  # \zeta(\mathfrak c) &= \xi^{c_0}\end{align} if the model has compositional
  # fields and equals one otherwise. $\xi$ corresponds to the parameter
  # ``Composition viscosity prefactor'' in the input file.
  # 
  # Finally, in the formula for the density, $\alpha$ corresponds to the
  # ``Thermal expansion coefficient'' and $\Delta\rho$ corresponds to the
  # parameter ``Density differential for compositional field 1''.
  # 
  # Note that this model uses the formulation that assumes an incompressible
  # medium despite the fact that the density follows the law
  # $\rho(T)=\rho_0(1-\alpha(T-T_{\text{ref}}))$.
  # 
  # \note{Despite its name, this material model is not exactly ``simple'', as
  # indicated by the formulas above. While it was originally intended to be
  # simple, it has over time acquired all sorts of temperature and
  # compositional dependencies that weren't initially intended. Consequently,
  # there is now a ``simpler'' material model that now fills the role the
  # current model was originally intended to fill.}
  # 
  # `simple compressible': A material model that has constant values for all
  # coefficients but the density. The defaults for all coefficients are chosen
  # to be similar to what is believed to be correct for Earth's mantle. All of
  # the values that define this model are read from a section ``Material
  # model/Simple compressible model'' in the input file, see
  # Section~\ref{parameters:Material_20model/Simple_20compressible_20model}.
  # 
  # This model uses the following equations for the density: \begin{align}
  # \rho(p,T) = \rho_0              \left(1-\alpha (T-T_a)\right)
  # \exp{\beta (P-P_0))}\end{align}This formulation for the density assumes
  # that the compressibility provided by the user is the adiabatic
  # compressibility ($\beta_S$). The thermal expansivity and isentropic
  # compressibility implied by the pressure and temperature dependence are
  # equal to the user-defined constant values only along the reference
  # isentrope, and there is also an implicit pressure dependence to the heat
  # capacity $C_p$ via Maxwell's relations.
  # 
  # `simpler': A material model that has constant values except for density,
  # which depends linearly on temperature: \begin{align}  \rho(p,T) &=
  # \left(1-\alpha (T-T_0)\right)\rho_0.\end{align}
  # 
  # \note{This material model fills the role the ``simple'' material model was
  # originally intended to fill, before the latter acquired all sorts of
  # complicated temperature and compositional dependencies.}
  # 
  # `visco plastic': An implementation of an incompressible
  # visco(elastic)-plastic rheology with options for selecting dislocation
  # creep, diffusion creep or composite viscous flow laws. Prior to yielding,
  # one may select to modify the viscosity to account for viscoelastic
  # effects. Plasticity limits viscous stresses through a Drucker Prager yield
  # criterion. Note that this material model is based heavily on the
  # DiffusionDislocation (Bob Myhill), DruckerPrager (Anne Glerum), and
  # Viscoelastic (John Naliboff) material models.
  # 
  # The viscosity for dislocation or diffusion creep is defined as \[v = \frac
  # 12 A^{-\frac{1}{n}} d^{\frac{m}{n}} \dot{\varepsilon}_{ii}^{\frac{1-n}{n}}
  # \exp\left(\frac{E + PV}{nRT}\right)\] where $A$ is the prefactor, $n$ is
  # the stress exponent, $\dot{\varepsilon}_{ii}$ is the square root of the
  # deviatoric strain rate tensor second invariant, $d$ is grain size, $m$ is
  # the grain size exponent, $E$ is activation energy, $V$ is activation
  # volume, $P$ is pressure, $R$ is the gas exponent and $T$ is temperature.
  # This form of the viscosity equation is commonly used in geodynamic
  # simulations. See, for example, Billen and Hirth (2007), G3, 8, Q08012.
  # Significantly, other studies may use slightly different forms of the
  # viscosity equation leading to variations in how specific terms are defined
  # or combined. For example, the grain size exponent should always be
  # positive in the diffusion viscosity equation used here, while other
  # studies place the grain size term in the denominator and invert the sign
  # of the grain size exponent. When examining previous work, one should
  # carefully check how the viscous prefactor and grain size terms are
  # defined.
  # 
  # One may select to use the diffusion ($v_{\text{diff}}$; $n=1$, $m!=0$),
  # dislocation ($v_{\text{disl}}$, $n>1$, $m=0$) or composite
  # $\frac{v_{\text{diff}} v_{\text{disl}}}{v_{\text{diff}}+v_{\text{disl}}}$
  # equation form.
  # 
  # The diffusion and dislocation prefactors can be weakened with a factor
  # between 0 and 1 according to the total or the viscous strain only.
  # 
  # Viscosity is limited through one of two different `yielding' mechanisms.
  # 
  # The first plasticity mechanism limits viscous stress through a Drucker
  # Prager yield criterion, where the yield stress in 3D is  $\sigma_y =
  # \frac{6C\cos(\phi) + 2P\sin(\phi)} {\sqrt(3)(3+\sin(\phi))}$ and $\sigma_y
  # = C\cos(\phi) + P\sin(\phi)$ in 2D. Above, $C$ is cohesion and $\phi$  is
  # the angle of internal friction.  Note that the 2D form is equivalent to
  # the Mohr Coulomb yield surface.  If $\phi$ is 0, the yield stress is fixed
  # and equal to the cohesion (Von Mises yield criterion). When the viscous
  # stress ($2v{\varepsilon}_{ii}$) exceeds the yield stress, the viscosity is
  # rescaled back to the yield surface:
  # $v_{y}=\sigma_{y}/(2{\varepsilon}_{ii})$. This form of plasticity is
  # commonly used in geodynamic models. See, for example, Thieulot, C. (2011),
  # PEPI 188, pp. 47-68.
  # 
  # The user has the option to linearly reduce the cohesion and internal
  # friction angle as a function of the finite strain magnitude. The finite
  # strain invariant or full strain tensor is calculated through compositional
  # fields within the material model. This implementation is identical to the
  # compositional field finite strain plugin and cookbook described in the
  # manual (author: Gassmoeller, Dannberg). If the user selects to track the
  # finite strain invariant ($e_{ii}$), a single compositional field tracks
  # the value derived from $e_{ii}^t = (e_{ii})^{(t-1)} + \dot{e}_{ii}\; dt$,
  # where $t$ and $t-1$ are the current and prior time steps, $\dot{e}_{ii}$
  # is the second invariant of the strain rate tensor and $dt$ is the time
  # step size. In the case of the full strain tensor $F$, the finite strain
  # magnitude is derived from the second invariant of the symmetric stretching
  # tensor $L$, where $L = F [F]^T$. The user must specify a single
  # compositional field for the finite strain invariant or multiple fields (4
  # in 2D, 9 in 3D) for the finite strain tensor. These field(s) must be the
  # first listed compositional fields in the parameter file. Note that one or
  # more of the finite strain tensor components must be assigned a non-zero
  # value initially. This value can be be quite small (e.g., 1.e-8), but still
  # non-zero. While the option to track and use the full finite strain tensor
  # exists, tracking the associated compositional fields is computationally
  # expensive in 3D. Similarly, the finite strain magnitudes may in fact
  # decrease if the orientation of the deformation field switches through
  # time. Consequently, the ideal solution is track the finite strain
  # invariant (single compositional) field within the material and track the
  # full finite strain tensor through particles.When only the second invariant
  # of the strain is tracked, one has the option to track the full strain or
  # only the plastic strain. In the latter case, strain is only tracked in
  # case the material is plastically yielding, i.e. the viscous stress > yield
  # stress.
  # 
  # Viscous stress may also be limited by a non-linear stress limiter that has
  # a form similar to the Peierls creep mechanism. This stress limiter assigns
  # an effective viscosity $\sigma_{\text{eff}} =
  # \frac{\tau_y}{2\varepsilon_y}
  # {\frac{\varepsilon_{ii}}{\varepsilon_y}}^{\frac{1}{n_y}-1}$ Above $\tau_y$
  # is a yield stress, $\varepsilon_y$ is the reference strain rate,
  # $\varepsilon_{ii}$ is the strain rate and $n_y$ is the stress limiter
  # exponent.  The yield stress, $\tau_y$, is defined through the Drucker
  # Prager yield criterion formulation. This method of limiting viscous stress
  # has been used in various forms within the geodynamic literature
  # \cite{chri92,vavv02,cibi13,cibi15}.When $n_y$ is 1, it essentially becomes
  # a linear viscosity model, and in the limit $n_y\rightarrow \infty$ it
  # converges to the standard viscosity rescaling method (concretely, values
  # $n_y>20$ are large enough).
  # 
  # The visco-plastic rheology described above may also be modified to include
  # viscoelastic deformation, thus producing a viscoelastic plastic
  # constitutive relationship.
  # 
  # The viscoelastic rheology behavior takes into account the elastic shear
  # strength (e.g., shear modulus), while the tensile and volumetric strength
  # (e.g., Young's and bulk modulus) are not considered. The model is
  # incompressible and allows specifying an arbitrary number of compositional
  # fields, where each field represents a different rock type or component of
  # the viscoelastic stress tensor. The stress tensor in 2D and 3D,
  # respectively, contains 3 or 6 components. The compositional fields
  # representing these components must be named and listed in a very specific
  # format, which is designed to minimize mislabeling stress tensor components
  # as distinct 'compositional rock types' (or vice versa). For 2D models, the
  # first three compositional fields must be labeled 'stress\_xx',
  # 'stress\_yy' and 'stress\_xy'. In 3D, the first six compositional fields
  # must be labeled 'stress\_xx', 'stress\_yy', 'stress\_zz', 'stress\_xy',
  # 'stress\_xz', 'stress\_yz'.
  # 
  # Combining this viscoelasticity implementation with non-linear viscous flow
  # and plasticity produces a constitutive relationship commonly referred to
  # as partial elastoviscoplastic (e.g., pEVP) in the geodynamics community.
  # While extensively discussed and applied within the geodynamics literature,
  # notable references include: Moresi et al. (2003), J. Comp. Phys., v. 184,
  # p. 476-497. Gerya and Yuen (2007), Phys. Earth. Planet. Inter., v. 163, p.
  # 83-105. Gerya (2010), Introduction to Numerical Geodynamic Modeling. Kaus
  # (2010), Tectonophysics, v. 484, p. 36-47. Choi et al. (2013), J. Geophys.
  # Res., v. 118, p. 2429-2444. Keller et al. (2013), Geophys. J. Int., v.
  # 195, p. 1406-1442.
  # 
  # The overview below directly follows Moresi et al. (2003) eqns. 23-38.
  # However, an important distinction between this material model and the
  # studies above is the use of compositional fields, rather than particles,
  # to track individual components of the viscoelastic stress tensor. The
  # material model will be updated when an option to track and calculate
  # viscoelastic stresses with particles is implemented.
  # 
  # Moresi et al. (2003) begins (eqn. 23) by writing the deviatoric rate of
  # deformation ($\hat{D}$) as the sum of elastic ($\hat{D_{e}}$) and viscous
  # ($\hat{D_{v}}$) components: $\hat{D} = \hat{D_{e}} + \hat{D_{v}}$.  These
  # terms further decompose into $\hat{D_{v}} = \frac{\tau}{2\eta}$ and
  # $\hat{D_{e}} = \frac{\overset{\nabla}{\tau}}{2\mu}$, where $\tau$ is the
  # viscous deviatoric stress, $\eta$ is the shear viscosity, $\mu$ is the
  # shear modulus and $\overset{\nabla}{\tau}$ is the Jaumann corotational
  # stress rate. This later term (eqn. 24) contains the time derivative of the
  # deviatoric stress ($\dot{\tau}$) and terms that account for material spin
  # (e.g., rotation) due to advection: $\overset{\nabla}{\tau} = \dot{\tau} +
  # {\tau}W -W\tau$. Above, $W$ is the material spin tensor (eqn. 25): $W_{ij}
  # = \frac{1}{2} \left (\frac{\partial V_{i}}{\partial x_{j}} -
  # \frac{\partial V_{j}}{\partial x_{i}} \right )$.
  # 
  # If plasticity is included, the deviatoric rate of deformation may be
  # written as: $\hat{D} = \hat{D_{e}} + \hat{D_{v}} + \hat{D_{p}}$, where
  # $\hat{D_{p}}$ is the plastic component. $\hat{D_{p}}$ decomposes to
  # $\frac{\tau_{y}}{2\eta_{y}}$, where $\tau_{y}$ is the yield stress and
  # $\eta_{y}$ is the viscosity rescaled to the yield surface. The Jaumann
  # stress-rate can also be approximated using terms from the previous time
  # step ($t$) and current time step ($t + \Delta t^{e}$):
  # $\smash[t]{\overset{\nabla}{\tau}}^{t + \Delta t^{e}} \approx
  # \frac{\tau^{t + \Delta t^{e} - \tau^{t}}}{\Delta t^{e}} - W^{t}\tau^{t} +
  # \tau^{t}W^{t}$. In this material model, the size of the time step above
  # ($\Delta t^{e}$) can be specified as the numerical time step size or an
  # independent fixed time step. If the latter case is selected, the user has
  # an option to apply a stress averaging scheme to account for the
  # differences between the numerical and fixed elastic time step (eqn. 32).
  # If one selects to use a fixed elastic time step throughout the model run,
  # this can still be achieved by using CFL and maximum time step values that
  # restrict the numerical time step to a specific time.
  # 
  # The formulation above allows rewriting the total rate of deformation (eqn.
  # 29) as
  # $\tau^{t + \Delta t^{e}} = \eta_{eff} \left ( 2\hat{D}^{t + \triangle
  # t^{e}} + \frac{\tau^{t}}{\mu \Delta t^{e}} + \frac{W^{t}\tau^{t} -
  # \tau^{t}W^{t}}{\mu}  \right )$.
  # 
  # The effective viscosity (eqn. 28) is a function of the viscosity ($\eta$),
  # elastic time step size ($\Delta t^{e}$) and shear relaxation time ($
  # \alpha = \frac{\eta}{\mu} $): $\eta_{eff} = \eta \frac{\Delta
  # t^{e}}{\Delta t^{e} + \alpha}$ The magnitude of the shear modulus thus
  # controls how much the effective viscosity is reduced relative to the
  # initial viscosity.
  # 
  # Elastic effects are introduced into the governing Stokes equations through
  # an elastic force term (eqn. 30) using stresses from the previous time
  # step: $F^{e,t} = -\frac{\eta_{eff}}{\mu \Delta t^{e}} \tau^{t}$. This
  # force term is added onto the right-hand side force vector in the system of
  # equations.
  # 
  # When plastic yielding occurs, the effective viscosity in equation 29 and
  # 30 is the plastic viscosity (equation 36). If the current stress is below
  # the plastic yield stress, the effective viscosity is still as defined in
  # equation 28. During non-linear iterations, we define the current stress
  # prior to yielding (e.g., value compared to yield stress) as $\tau^{t +
  # \Delta t^{e}} = \eta_{eff} \left ( 2\hat{D}^{t + \triangle t^{e}} +
  # \frac{\tau^{t}}{\mu \Delta t^{e}} \right ) $
  # 
  # Compositional fields can each be assigned individual values of thermal
  # diffusivity, heat capacity, density, thermal expansivity and rheological
  # parameters.
  # 
  # If more than one compositional field is present at a given point,
  # viscosities are averaged with an arithmetic, geometric harmonic (default)
  # or maximum composition scheme.
  # 
  # The value for the components of this formula and additional parameters are
  # read from the parameter file in subsection  'Material model/Visco
  # Plastic'.
  # 
  # `viscoelastic': An implementation of a simple linear viscoelastic rheology
  # that only includes the deviatoric components of elasticity. Specifically,
  # the viscoelastic rheology only takes into account the elastic shear
  # strength (e.g., shear modulus), while the tensile and volumetric strength
  # (e.g., Young's and bulk modulus) are not considered. The model is
  # incompressible and allows specifying an arbitrary number of compositional
  # fields, where each field represents a different rock type or component of
  # the viscoelastic stress tensor. The stress tensor in 2D and 3D,
  # respectively, contains 3 or 6 components. The compositional fields
  # representing these components must be named and listed in a very specific
  # format, which is designed to minimize mislabeling stress tensor components
  # as distinct 'compositional rock types' (or vice versa). For 2D models, the
  # first three compositional fields must be labeled 'stress\_xx',
  # 'stress\_yy' and 'stress\_xy'. In 3D, the first six compositional fields
  # must be labeled 'stress\_xx', 'stress\_yy', 'stress\_zz', 'stress\_xy',
  # 'stress\_xz', 'stress\_yz'.
  # 
  # Expanding the model to include non-linear viscous flow (e.g.,
  # diffusion/dislocation creep) and plasticity would produce a constitutive
  # relationship commonly referred to as partial elastoviscoplastic (e.g.,
  # pEVP) in the geodynamics community. While extensively discussed and
  # applied within the geodynamics literature, notable references include:
  # Moresi et al. (2003), J. Comp. Phys., v. 184, p. 476-497. Gerya and Yuen
  # (2007), Phys. Earth. Planet. Inter., v. 163, p. 83-105. Gerya (2010),
  # Introduction to Numerical Geodynamic Modeling. Kaus (2010),
  # Tectonophysics, v. 484, p. 36-47. Choi et al. (2013), J. Geophys. Res., v.
  # 118, p. 2429-2444. Keller et al. (2013), Geophys. J. Int., v. 195, p.
  # 1406-1442.
  # 
  # The overview below directly follows Moresi et al. (2003) eqns. 23-32.
  # However, an important distinction between this material model and the
  # studies above is the use of compositional fields, rather than particles,
  # to track individual components of the viscoelastic stress tensor. The
  # material model will be updated when an option to track and calculate
  # viscoelastic stresses with particles is implemented.
  # 
  # Moresi et al. (2003) begins (eqn. 23) by writing the deviatoric rate of
  # deformation ($\hat{D}$) as the sum of elastic ($\hat{D_{e}}$) and viscous
  # ($\hat{D_{v}}$) components: $\hat{D} = \hat{D_{e}} + \hat{D_{v}}$.  These
  # terms further decompose into $\hat{D_{v}} = \frac{\tau}{2\eta}$ and
  # $\hat{D_{e}} = \frac{\overset{\nabla}{\tau}}{2\mu}$, where $\tau$ is the
  # viscous deviatoric stress, $\eta$ is the shear viscosity, $\mu$ is the
  # shear modulus and $\overset{\nabla}{\tau}$ is the Jaumann corotational
  # stress rate. This later term (eqn. 24) contains the time derivative of the
  # deviatoric stress ($\dot{\tau}$) and terms that account for material spin
  # (e.g., rotation) due to advection: $\overset{\nabla}{\tau} = \dot{\tau} +
  # {\tau}W -W\tau$. Above, $W$ is the material spin tensor (eqn. 25): $W_{ij}
  # = \frac{1}{2} \left (\frac{\partial V_{i}}{\partial x_{j}} -
  # \frac{\partial V_{j}}{\partial x_{i}} \right )$.
  # 
  # The Jaumann stress-rate can also be approximated using terms from the
  # previous time step ($t$) and current time step ($t + \Delta t^{e}$):
  # $\smash[t]{\overset{\nabla}{\tau}}^{t + \Delta t^{e}} \approx
  # \frac{\tau^{t + \Delta t^{e} - \tau^{t}}}{\Delta t^{e}} - W^{t}\tau^{t} +
  # \tau^{t}W^{t}$. In this material model, the size of the time step above
  # ($\Delta t^{e}$) can be specified as the numerical time step size or an
  # independent fixed time step. If the latter case is selected, the user has
  # an option to apply a stress averaging scheme to account for the
  # differences between the numerical and fixed elastic time step (eqn. 32).
  # If one selects to use a fixed elastic time step throughout the model run,
  # this can still be achieved by using CFL and maximum time step values that
  # restrict the numerical time step to a specific time.
  # 
  # The formulation above allows rewriting the total deviatoric stress (eqn.
  # 29) as
  # $\tau^{t + \Delta t^{e}} = \eta_{eff} \left ( 2\hat{D}^{t + \triangle
  # t^{e}} + \frac{\tau^{t}}{\mu \Delta t^{e}} + \frac{W^{t}\tau^{t} -
  # \tau^{t}W^{t}}{\mu}  \right )$.
  # 
  # The effective viscosity (eqn. 28) is a function of the viscosity ($\eta$),
  # elastic time step size ($\Delta t^{e}$) and shear relaxation time ($
  # \alpha = \frac{\eta}{\mu} $): $\eta_{eff} = \eta \frac{\Delta
  # t^{e}}{\Delta t^{e} + \alpha}$ The magnitude of the shear modulus thus
  # controls how much the effective viscosity is reduced relative to the
  # initial viscosity.
  # 
  # Elastic effects are introduced into the governing Stokes equations through
  # an elastic force term (eqn. 30) using stresses from the previous time
  # step: $F^{e,t} = -\frac{\eta_{eff}}{\mu \Delta t^{e}} \tau^{t}$. This
  # force term is added onto the right-hand side force vector in the system of
  # equations.
  # 
  # The value of each compositional field representing distinct rock types at
  # a point is interpreted to be a volume fraction of that rock type. If the
  # sum of the compositional field volume fractions is less than one, then the
  # remainder of the volume is assumed to be 'background material'.
  # 
  # Several model parameters (densities, elastic shear moduli, thermal
  # expansivities, thermal conductivies, specific heats) can be defined
  # per-compositional field. For each material parameter the user supplies a
  # comma delimited list of length N+1, where N is the number of compositional
  # fields. The additional field corresponds to the value for background
  # material. They should be ordered ''background, composition1,
  # composition2...''. However, the first 3 (2D) or 6 (3D) composition fields
  # correspond to components of the elastic stress tensor and their material
  # values will not contribute to the volume fractions. If a single value is
  # given, then all the compositional fields are given that value. Other
  # lengths of lists are not allowed. For a given compositional field the
  # material parameters are treated as constant, except density, which varies
  # linearly with temperature according to the thermal expansivity.
  # 
  # When more than one compositional field is present at a point, they are
  # averaged arithmetically. An exception is viscosity, which may be averaged
  # arithmetically, harmonically, geometrically, or by selecting the viscosity
  # of the composition field with the greatest volume fraction.
  set Model name         = simple # default: unspecified


  subsection Ascii reference profile
    # Reference conductivity
    set Thermal conductivity       = 4.0

    # The temperature dependence of viscosity. Dimensionless exponent.
    set Thermal viscosity exponent = 0.

    # A list of depths where the viscosity changes. Values must monotonically
    # increase. Units: \si{\meter}.
    set Transition depths          = 1.5e5, 4.1e5, 6.6e5

    # Whether to use the TALA instead of the ALA approximation.
    set Use TALA                   = false

    # Viscosity
    set Viscosity                  = 1e21

    # A list of prefactors for the viscosity that determine the viscosity
    # profile. Each prefactor is applied in a depth range specified by the
    # list of `Transition depths', i.e. the first prefactor is applied above
    # the first transition depth, the second one between the first and second
    # transition depth, and so on. To compute the viscosity profile, this
    # prefactor is multiplied by the reference viscosity specified through the
    # parameter `Viscosity'. List must have one more entry than Transition
    # depths. Units: non-dimensional.
    set Viscosity prefactors       = 10., 0.1, 1., 10.


    subsection Ascii data model
      # The name of a directory that contains the model data. This path may
      # either be absolute (if starting with a `/') or relative to the current
      # directory. The path may also include the special text
      # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
      # the ASPECT source files were located when ASPECT was compiled. This
      # interpretation allows, for example, to reference files located in the
      # `data/' subdirectory of ASPECT.
      set Data directory = $ASPECT_SOURCE_DIR/data/adiabatic-conditions/ascii-data/

      # The file name of the model data.
      set Data file name = 

      # Scalar factor, which is applied to the model data. You might want to
      # use this to scale the input to a reference model. Another way to use
      # this factor is to convert units of the input files. For instance, if
      # you provide velocities in cm/yr set this factor to 0.01.
      set Scale factor   = 1.
    end

  end

  subsection Averaging
    # Choose the averaging operation to use.
    set Averaging operation = none

    # The name of a material model that will be modified by an averaging
    # operation. Valid values for this parameter are the names of models that
    # are also valid for the ``Material models/Model name'' parameter. See the
    # documentation for that for more information.
    set Base model          = simple

    # The limit normalized distance between 0 and 1 where the bell shape
    # becomes zero. See the manual for a more information.
    set Bell shape limit    = 1.
  end

  subsection Compositing
    # Material model to use for Compressibility. Valid values for this
    # parameter are the names of models that are also valid for the ``Material
    # models/Model name'' parameter. See the documentation for that for more
    # information.
    set Compressibility                = unspecified

    # Material model to use for Density. Valid values for this parameter are
    # the names of models that are also valid for the ``Material models/Model
    # name'' parameter. See the documentation for that for more information.
    set Density                        = unspecified

    # Material model to use for Entropy derivative pressure. Valid values for
    # this parameter are the names of models that are also valid for the
    # ``Material models/Model name'' parameter. See the documentation for that
    # for more information.
    set Entropy derivative pressure    = unspecified

    # Material model to use for Entropy derivative temperature. Valid values
    # for this parameter are the names of models that are also valid for the
    # ``Material models/Model name'' parameter. See the documentation for that
    # for more information.
    set Entropy derivative temperature = unspecified

    # Material model to use for Reaction terms. Valid values for this
    # parameter are the names of models that are also valid for the ``Material
    # models/Model name'' parameter. See the documentation for that for more
    # information.
    set Reaction terms                 = unspecified

    # Material model to use for Specific heat. Valid values for this parameter
    # are the names of models that are also valid for the ``Material
    # models/Model name'' parameter. See the documentation for that for more
    # information.
    set Specific heat                  = unspecified

    # Material model to use for Thermal conductivity. Valid values for this
    # parameter are the names of models that are also valid for the ``Material
    # models/Model name'' parameter. See the documentation for that for more
    # information.
    set Thermal conductivity           = unspecified

    # Material model to use for Thermal expansion coefficient. Valid values
    # for this parameter are the names of models that are also valid for the
    # ``Material models/Model name'' parameter. See the documentation for that
    # for more information.
    set Thermal expansion coefficient  = unspecified

    # Material model to use for Viscosity. Valid values for this parameter are
    # the names of models that are also valid for the ``Material models/Model
    # name'' parameter. See the documentation for that for more information.
    set Viscosity                      = unspecified
  end

  subsection Composition reaction model
    # A linear dependency of viscosity on the first compositional field.
    # Dimensionless prefactor. With a value of 1.0 (the default) the viscosity
    # does not depend on the composition.
    set Composition viscosity prefactor 1              = 1.0

    # A linear dependency of viscosity on the second compositional field.
    # Dimensionless prefactor. With a value of 1.0 (the default) the viscosity
    # does not depend on the composition.
    set Composition viscosity prefactor 2              = 1.0

    # If compositional fields are used, then one would frequently want to make
    # the density depend on these fields. In this simple material model, we
    # make the following assumptions: if no compositional fields are used in
    # the current simulation, then the density is simply the usual one with
    # its linear dependence on the temperature. If there are compositional
    # fields, then the material model determines how many of them influence
    # the density. The composition-dependence adds a term of the kind $+\Delta
    # \rho \; c_1(\mathbf x)$. This parameter describes the value of $\Delta
    # \rho$. Units: \si{\kilogram\per\meter\cubed}/unit change in
    # composition.
    set Density differential for compositional field 1 = 0.

    # If compositional fields are used, then one would frequently want to make
    # the density depend on these fields. In this simple material model, we
    # make the following assumptions: if no compositional fields are used in
    # the current simulation, then the density is simply the usual one with
    # its linear dependence on the temperature. If there are compositional
    # fields, then the material model determines how many of them influence
    # the density. The composition-dependence adds a term of the kind $+\Delta
    # \rho \; c_2(\mathbf x)$. This parameter describes the value of $\Delta
    # \rho$. Units: \si{\kilogram\per\meter\cubed}/unit change in
    # composition.
    set Density differential for compositional field 2 = 0.

    # Above this depth the compositional fields react: The first field gets
    # converted to the second field. Units: \si{\meter}.
    set Reaction depth                                 = 0.

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density                              = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                        = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature                          = 293.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                           = 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient                  = 2e-5

    # The temperature dependence of viscosity. Dimensionless exponent.
    set Thermal viscosity exponent                     = 0.0

    # The value of the constant viscosity. Units:
    # \si{\kilogram\per\meter\per\second}.
    set Viscosity                                      = 5e24
  end

  subsection Depth dependent model
    # The name of a material model that will be modified by a depth dependent
    # viscosity. Valid values for this parameter are the names of models that
    # are also valid for the ``Material models/Model name'' parameter. See the
    # documentation for that for more information.
    set Base model              = simple

    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory          = $ASPECT_SOURCE_DIR/data/material-model/rheology/

    # The file name of the model data.
    set Data file name          = ascii_depth_profile.txt

    # Method that is used to specify how the viscosity should vary with
    # depth.
    set Depth dependence method = None

    # A comma-separated list of depth values for use with the ``List'' ``Depth
    # dependence method''. The list must be provided in order of increasing
    # depth, and the last value must be greater than or equal to the maximal
    # depth of the model. The depth list is interpreted as a layered viscosity
    # structure and the depth values specify the maximum depths of each
    # layer.
    set Depth list              = 

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor            = 1.

    # A comma-separated list of viscosity values, corresponding to the depth
    # values provided in ``Depth list''. The number of viscosity values
    # specified here must be the same as the number of depths provided in
    # ``Depth list''.
    set Viscosity list          = 


    subsection Viscosity depth function
      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants  = 
      set Function expression = 1.0e21

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names      = x,t
    end

  end

  subsection Diffusion dislocation
    # List of activation energies, $E_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\joule\per\mole}.
    set Activation energies for diffusion creep   = 375e3

    # List of activation energies, $E_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\joule\per\mole}.
    set Activation energies for dislocation creep = 530e3

    # List of activation volumes, $V_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\meter\cubed\per\mole}.
    set Activation volumes for diffusion creep    = 6e-6

    # List of activation volumes, $V_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\meter\cubed\per\mole}.
    set Activation volumes for dislocation creep  = 1.4e-5

    # List of densities, $\rho$, for background mantle and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value. Units: \si{\kilogram\per\meter\cubed}.
    set Densities                                 = 3300.

    # Scaling coefficient for effective viscosity.
    set Effective viscosity coefficient           = 1.0

    # Units: \si{\meter}.
    set Grain size                                = 1e-3

    # List of grain size exponents, $m_{\text{diffusion}}$, for background
    # material and compositional fields, for a total of N+1 values, where N is
    # the number of compositional fields. If only one value is given, then all
    # use the same value. Units: None.
    set Grain size exponents for diffusion creep  = 3.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Heat capacity                             = 1.25e3

    # Maximum number of iterations to find the correct diffusion/dislocation
    # strain rate ratio.
    set Maximum strain rate ratio iterations      = 40

    # Upper cutoff for effective viscosity. Units: \si{\pascal\second}.
    set Maximum viscosity                         = 1e28

    # Stabilizes strain dependent viscosity. Units: \si{\per\second}.
    set Minimum strain rate                       = 1.4e-20

    # Lower cutoff for effective viscosity. Units: \si{\pascal\second}.
    set Minimum viscosity                         = 1e17

    # List of viscosity prefactors, $A$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units:
    # \si{\per\pascal\meter}$^{m_{\text{diffusion}}}$\si{\per\second}.
    set Prefactors for diffusion creep            = 1.5e-15

    # List of viscosity prefactors, $A$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\pascal}$^{-n_{\text{dislocation}}}$
    # \si{\per\second}.
    set Prefactors for dislocation creep          = 1.1e-16

    # For calculating density by thermal expansivity. Units: \si{\kelvin}.
    set Reference temperature                     = 293.

    # The reference viscosity that is used for pressure scaling. To understand
    # how pressure scaling works, take a look at \cite{KHB12}. In particular,
    # the value of this parameter would not affect the solution computed by
    # \aspect{} if we could do arithmetic exactly; however, computers do
    # arithmetic in finite precision, and consequently we need to scale
    # quantities in ways so that their magnitudes are roughly the same. As
    # explained in \cite{KHB12}, we scale the pressure during some
    # computations (never visible by users) by a factor that involves a
    # reference viscosity. This parameter describes this reference viscosity.
    # 
    # For problems with a constant viscosity, you will generally want to
    # choose the reference viscosity equal to the actual viscosity. For
    # problems with a variable viscosity, the reference viscosity should be a
    # value that adequately represents the order of magnitude of the
    # viscosities that appear, such as an average value or the value one would
    # use to compute a Rayleigh number.
    # 
    # Units: \si{\pascal\second}.
    set Reference viscosity                       = 1e22

    # Tolerance for correct diffusion/dislocation strain rate ratio.
    set Strain rate residual tolerance            = 1e-22

    # List of stress exponents, $n_{\text{diffusion}}$, for background mantle
    # and compositional fields, for a total of N+1 values, where N is the
    # number of compositional fields. The stress exponent for diffusion creep
    # is almost always equal to one. If only one value is given, then all use
    # the same value.  Units: None.
    set Stress exponents for diffusion creep      = 1.

    # List of stress exponents, $n_{\text{dislocation}}$, for background
    # material and compositional fields, for a total of N+1 values, where N is
    # the number of compositional fields. If only one value is given, then all
    # use the same value.  Units: None.
    set Stress exponents for dislocation creep    = 3.5

    # Units: \si{\meter\squared\per\second}.
    set Thermal diffusivity                       = 0.8e-6

    # List of thermal expansivities for background mantle and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value.  Units: \si{\per\kelvin}.
    set Thermal expansivities                     = 3.5e-5

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme                = harmonic
  end

  subsection Drucker Prager
    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density             = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat       = 1250.

    # The reference temperature $T_0$. The reference temperature is used in
    # the density calculation. Units: \si{\kelvin}.
    set Reference temperature         = 293.

    # The reference viscosity that is used for pressure scaling. To understand
    # how pressure scaling works, take a look at \cite{KHB12}. In particular,
    # the value of this parameter would not affect the solution computed by
    # \aspect{} if we could do arithmetic exactly; however, computers do
    # arithmetic in finite precision, and consequently we need to scale
    # quantities in ways so that their magnitudes are roughly the same. As
    # explained in \cite{KHB12}, we scale the pressure during some
    # computations (never visible by users) by a factor that involves a
    # reference viscosity. This parameter describes this reference viscosity.
    # 
    # For problems with a constant viscosity, you will generally want to
    # choose the reference viscosity equal to the actual viscosity. For
    # problems with a variable viscosity, the reference viscosity should be a
    # value that adequately represents the order of magnitude of the
    # viscosities that appear, such as an average value or the value one would
    # use to compute a Rayleigh number.
    # 
    # Units: \si{\pascal\second}.
    set Reference viscosity           = 1e22

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity          = 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient = 2e-5


    subsection Viscosity
      # The value of the angle of internal friction $\phi$. For a value of
      # zero, in 2D the von Mises criterion is retrieved. Angles higher than
      # 30 degrees are harder to solve numerically. Units: degrees.
      set Angle of internal friction = 0.

      # The value of the cohesion $C$. Units: \si{\pascal}.
      set Cohesion                   = 2e7

      # The value of the maximum viscosity cutoff $\eta_max$. Units:
      # \si{\pascal\second}.
      set Maximum viscosity          = 1e24

      # The value of the minimum viscosity cutoff $\eta_min$. Units:
      # \si{\pascal\second}.
      set Minimum viscosity          = 1e19

      # The value of the initial strain rate prescribed during the first
      # nonlinear iteration $\dot{\epsilon}_ref$. Units: \si{\per\second}.
      set Reference strain rate      = 1e-15
    end

  end

  subsection Dynamic Friction
    # List of densities for background mantle and compositional fields,for a
    # total of N+M+1 values, where N is the number of compositional fields and
    # M is the number of phases. If only one value is given, then all use the
    # same value. Units: \si{\kilogram\per\meter\cubed}.
    set Densities                  = 3300.

    # List of specific heats $C_p$ for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Heat capacities            = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature      = 293.

    # List of thermal conductivities for background mantle and compositional
    # fields,for a total of N+1 values, where N is the number of compositional
    # fields.If only one value is given, then all use the same value. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivities     = 4.7

    # List of thermal expansivities for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units: \si{\per\kelvin}.
    set Thermal expansivities      = 0.000040

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme = harmonic


    subsection Viscosities
      # List of background viscosities for mantle and compositional fields,for
      # a total of N+1 values, where N is the number of compositional
      # fields.If only one value is given, then all use the same value. Units:
      # \si{\pascal\second}.
      set Background Viscosities           = 1.e20

      # List of coefficients of dynamic friction for background mantle and
      # compositional fields,for a total of N+1 values, where N is the number
      # of compositional fields.If only one value is given, then all use the
      # same value. Units: dimensionless.
      set Coefficients of dynamic friction = 0.4

      # List of coefficients of static friction for background mantle and
      # compositional fields,for a total of N+1 values, where N is the number
      # of compositional fields.If only one value is given, then all use the
      # same value. Units: dimensionless.
      set Coefficients of static friction  = 0.5

      # List of cohesions for background mantle and compositional fields,for a
      # total of N+1 values, where N is the number of compositional fields.If
      # only one value is given, then all use the same value. Units:
      # \si{\pascal}.
      set Cohesions                        = 4.e6

      # The value of the maximum viscosity cutoff $\eta_max$. Units:
      # \si{\pascal\second}.
      set Maximum viscosity                = 1e24

      # The value of the minimum viscosity cutoff $\eta_min$. Units:
      # \si{\pascal\second}.
      set Minimum viscosity                = 1e19

      # The value of the initial strain rate prescribed during the first
      # nonlinear iteration $\dot{\epsilon}_ref$. Units: \si{\per\second}.
      set Reference strain rate            = 1e-15
    end

  end

  subsection Grain size model
    # This parameter determines whether to advect the logarithm of the grain
    # size or the grain size itself. The equation and the physics are the
    # same, but for problems with high grain size gradients it might be
    # preferable to advect the logarithm.
    set Advect logarithm of grain size              = false

    # The average specific grain boundary energy $\gamma$. Units:
    # \si{\joule\per\meter\squared}.
    set Average specific grain boundary energy      = 1.0

    # This parameter determines whether to use bilinear interpolation to
    # compute material properties (slower but more accurate).
    set Bilinear interpolation                      = true

    # The path to the model data. The path may also include the special text
    # '$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # 'data/' subdirectory of ASPECT.
    set Data directory                              = $ASPECT_SOURCE_DIR/data/material-model/steinberger/

    # The file names of the enthalpy derivatives data. List with as many
    # components as active compositional fields (material data is assumed to
    # be in order with the ordering of the fields).
    set Derivatives file names                      = 

    # The activation energy for diffusion creep $E_{diff}$. Units:
    # \si{\joule\per\mole}.
    set Diffusion activation energy                 = 3.35e5

    # The activation volume for diffusion creep $V_{diff}$. Units:
    # \si{\meter\cubed\per\mole}.
    set Diffusion activation volume                 = 4e-6

    # The power-law exponent $n_{diff}$ for diffusion creep. Units: none.
    set Diffusion creep exponent                    = 1.

    # The diffusion creep grain size exponent $p_{diff}$ that determines the
    # dependence of viscosity on grain size. Units: none.
    set Diffusion creep grain size exponent         = 3.

    # The prefactor for the diffusion creep law $A_{diff}$. Units:
    # \si{\meter}$^{p_{diff}}$\si{\pascal}$^{-n_{diff}}$\si{\per\second}.
    set Diffusion creep prefactor                   = 7.4e-15

    # The activation energy for dislocation creep $E_{dis}$. Units:
    # \si{\joule\per\mole}.
    set Dislocation activation energy               = 4.8e5

    # The activation volume for dislocation creep $V_{dis}$. Units:
    # \si{\meter\cubed\per\mole}.
    set Dislocation activation volume               = 1.1e-5

    # The power-law exponent $n_{dis}$ for dislocation creep. Units: none.
    set Dislocation creep exponent                  = 3.5

    # The prefactor for the dislocation creep law $A_{dis}$. Units:
    # \si{\pascal}$^{-n_{dis}}$\si{\per\second}.
    set Dislocation creep prefactor                 = 4.5e-15

    # We need to perform an iteration inside the computation of the
    # dislocation viscosity, because it depends on the dislocation strain
    # rate, which depends on the dislocation viscosity itself. This number
    # determines the maximum number of iterations that are performed.
    set Dislocation viscosity iteration number      = 100

    # We need to perform an iteration inside the computation of the
    # dislocation viscosity, because it depends on the dislocation strain
    # rate, which depends on the dislocation viscosity itself. This number
    # determines the termination accuracy, i.e. if the dislocation viscosity
    # changes by less than this factor we terminate the iteration.
    set Dislocation viscosity iteration threshold   = 1e-3

    # The geometric constant $c$ used in the paleowattmeter grain size
    # reduction law. Units: none.
    set Geometric constant                          = 3.

    # The activation energy for grain growth $E_g$. Units:
    # \si{\joule\per\mole}.
    set Grain growth activation energy              = 3.5e5

    # The activation volume for grain growth $V_g$. Units:
    # \si{\meter\cubed\per\mole}.
    set Grain growth activation volume              = 8e-6

    # The exponent of the grain growth law $p_g$. This is an experimentally
    # determined grain growth constant. Units: none.
    set Grain growth exponent                       = 3.

    # The prefactor for the Ostwald ripening grain growth law $G_0$. This is
    # dependent on water content, which is assumed to be 50 H/$10^6$ Si for
    # the default value. Units: \si{\meter}$^{p_g}$\si{\per\second}.
    set Grain growth rate constant                  = 1.5e-5

    # A scaling factor for the grain size in the lower mantle. In models where
    # the high grain size contrast between the upper and lower mantle causes
    # numerical problems, the grain size in the lower mantle can be scaled to
    # a larger value, simultaneously scaling the viscosity prefactors and
    # grain growth parameters to keep the same physical behavior. Differences
    # to the original formulation only occur when material with a smaller
    # grain size than the recrystallization grain size cross the upper-lower
    # mantle boundary. The real grain size can be obtained by dividing the
    # model grain size by this value. Units: none.
    set Lower mantle grain size scaling             = 1.0

    # The material file format to be read in the property tables.
    set Material file format                        = perplex

    # The file names of the material data. List with as many components as
    # active compositional fields (material data is assumed to be in order
    # with the ordering of the fields).
    set Material file names                         = pyr-ringwood88.txt

    # The maximum number of substeps over the temperature pressure range to
    # calculate the averaged enthalpy gradient over a cell.
    set Maximum latent heat substeps                = 1

    # The maximum specific heat that is allowed in the whole model domain.
    # Units: J/kg/K.
    set Maximum specific heat                       = 6000.

    # The factor by which viscosity at adiabatic temperature and ambient
    # temperature are allowed to differ (a value of x means that the viscosity
    # can be x times higher or x times lower compared to the value at
    # adiabatic temperature. This parameter is introduced to limit local
    # viscosity contrasts, but still allow for a widely varying viscosity over
    # the whole mantle range. Units: none.
    set Maximum temperature dependence of viscosity = 100.

    # The maximum thermal expansivity that is allowed in the whole model
    # domain. Units: 1/K.
    set Maximum thermal expansivity                 = 1e-3

    # The maximum viscosity that is allowed in the whole model domain. Units:
    # Pa \, s.
    set Maximum viscosity                           = 1e26

    # The minimum grain size that is used for the material model. This
    # parameter is introduced to limit local viscosity contrasts, but still
    # allows for a widely varying viscosity over the whole mantle range.
    # Units: \si{\meter}.
    set Minimum grain size                          = 1e-5

    # The minimum specific heat that is allowed in the whole model domain.
    # Units: J/kg/K.
    set Minimum specific heat                       = 500.

    # The minimum thermal expansivity that is allowed in the whole model
    # domain. Units: 1/K.
    set Minimum thermal expansivity                 = 1e-5

    # The minimum viscosity that is allowed in the whole model domain. Units:
    # Pa \, s.
    set Minimum viscosity                           = 1e18

    # A list of Clapeyron slopes for each phase transition. A positive
    # Clapeyron slope indicates that the phase transition will occur in a
    # greater depth, if the temperature is higher than the one given in Phase
    # transition temperatures and in a smaller depth, if the temperature is
    # smaller than the one given in Phase transition temperatures. For
    # negative slopes the other way round. List must have the same number of
    # entries as Phase transition depths. Units: \si{\pascal\per\kelvin}.
    set Phase transition Clapeyron slopes           = 

    # A list of depths where phase transitions occur. Values must
    # monotonically increase. Units: \si{\meter}.
    set Phase transition depths                     = 

    # A list of temperatures where phase transitions occur. Higher or lower
    # temperatures lead to phase transition occurring in smaller or greater
    # depths than given in Phase transition depths, depending on the Clapeyron
    # slope given in Phase transition Clapeyron slopes. List must have the
    # same number of entries as Phase transition depths. Units: \si{\kelvin}.
    set Phase transition temperatures               = 

    # A list of widths for each phase transition. This is only use to specify
    # the region where the recrystallized grain size is assigned after
    # material has crossed a phase transition and should accordingly be chosen
    # similar to the maximum cell width expected at the phase transition.List
    # must have the same number of entries as Phase transition depths. Units:
    # \si{\meter}.
    set Phase transition widths                     = 

    # This parameter ($\lambda$) gives an estimate of the strain necessary to
    # achieve a new grain size.
    set Reciprocal required strain                  = 10.

    # The grain size $d_{ph}$ to that a phase will be reduced to when crossing
    # a phase transition. When set to zero, grain size will not be reduced.
    # Units: \si{\meter}.
    set Recrystallized grain size                   = 

    # The value of the reference compressibility. Units: \si{\per\pascal}.
    set Reference compressibility                   = 4e-12

    # The reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density                           = 3300

    # The value of the specific heat $cp$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                     = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature                       = 293.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                        = 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient               = 2e-5

    # This parameter determines whether to use the enthalpy to calculate the
    # thermal expansivity and specific heat (if true) or use the thermal
    # expansivity and specific heat values from the material properties table
    # directly (if false).
    set Use enthalpy for material properties        = true

    # A flag indicating whether the computation should be use the
    # paleowattmeter approach of Austin and Evans (2007) for grain size
    # reduction in the dislocation creep regime (if true) or the
    # paleopiezometer approach from Hall and Parmetier (2003) (if false).
    set Use paleowattmeter                          = true

    # This parameter determines whether to use the table properties also for
    # density, thermal expansivity and specific heat. If false the properties
    # are generated as in the simple compressible plugin.
    set Use table properties                        = false

    # The value of the constant viscosity. Units: \si{\pascal\second}.
    set Viscosity                                   = 5e24

    # The fraction $\chi$ of work done by dislocation creep to change the
    # grain boundary area. Units: \si{\joule\per\meter\squared}.
    set Work fraction for boundary area change      = 0.1
  end

  subsection Latent heat
    # A linear dependency of viscosity on composition. Dimensionless
    # prefactor.
    set Composition viscosity prefactor                = 1.0

    # The value of the compressibility $\kappa$. Units: \si{\per\pascal}.
    set Compressibility                                = 5.124e-12

    # A list of phases, which correspond to the Phase transition density
    # jumps. The density jumps occur only in the phase that is given by this
    # phase value. 0 stands for the 1st compositional fields, 1 for the second
    # compositional field and -1 for none of them. List must have the same
    # number of entries as Phase transition depths. Units:
    # \si{\pascal\per\kelvin}.
    set Corresponding phase for density jump           = 

    # Whether to list phase transitions by depth or pressure. If this
    # parameter is true, then the input file will use Phase transitions depths
    # and Phase transition widths to define the phase transition. If it is
    # false, the parameter file will read in phase transition data from Phase
    # transition pressures and Phase transition pressure widths.
    set Define transition by depth instead of pressure = true

    # If compositional fields are used, then one would frequently want to make
    # the density depend on these fields. In this simple material model, we
    # make the following assumptions: if no compositional fields are used in
    # the current simulation, then the density is simply the usual one with
    # its linear dependence on the temperature. If there are compositional
    # fields, then the density only depends on the first one in such a way
    # that the density has an additional term of the kind $+\Delta \rho \;
    # c_1(\mathbf x)$. This parameter describes the value of $\Delta \rho$.
    # Units: \si{\kilogram\per\meter\cubed}/unit change in composition.
    set Density differential for compositional field 1 = 0.

    # Limit for the maximum viscosity in the model. Units: Pa \, s.
    set Maximum viscosity                              = 1e24

    # Limit for the minimum viscosity in the model. Units: Pa \, s.
    set Minimum viscosity                              = 1e19

    # A list of Clapeyron slopes for each phase transition. A positive
    # Clapeyron slope indicates that the phase transition will occur in a
    # greater depth, if the temperature is higher than the one given in Phase
    # transition temperatures and in a smaller depth, if the temperature is
    # smaller than the one given in Phase transition temperatures. For
    # negative slopes the other way round. List must have the same number of
    # entries as Phase transition depths. Units: \si{\pascal\per\kelvin}.
    set Phase transition Clapeyron slopes              = 

    # A list of density jumps at each phase transition. A positive value means
    # that the density increases with depth. The corresponding entry in
    # Corresponding phase for density jump determines if the density jump
    # occurs in peridotite, eclogite or none of them.List must have the same
    # number of entries as Phase transition depths. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Phase transition density jumps                 = 

    # A list of depths where phase transitions occur. Values must
    # monotonically increase. Units: \si{\meter}.
    set Phase transition depths                        = 

    # A list of widths for each phase transition, in terms of pressure. The
    # phase functions are scaled with these values, leading to a jump between
    # phases for a value of zero and a gradual transition for larger values.
    # List must have the same number of entries as Phase transition pressures.
    # Define transition by depth instead of pressure must be set to false to
    # use this parameter. Units: \si{\pascal}.
    set Phase transition pressure widths               = 

    # A list of pressures where phase transitions occur. Values must
    # monotonically increase. Define transition by depth instead of pressure
    # must be set to false to use this parameter. Units: \si{\pascal}.
    set Phase transition pressures                     = 

    # A list of temperatures where phase transitions occur. Higher or lower
    # temperatures lead to phase transition occurring in smaller or greater
    # depths than given in Phase transition depths, depending on the Clapeyron
    # slope given in Phase transition Clapeyron slopes. List must have the
    # same number of entries as Phase transition depths. Units: \si{\kelvin}.
    set Phase transition temperatures                  = 

    # A list of widths for each phase transition, in terms of depth. The phase
    # functions are scaled with these values, leading to a jump between phases
    # for a value of zero and a gradual transition for larger values. List
    # must have the same number of entries as Phase transition depths. Units:
    # \si{\meter}.
    set Phase transition widths                        = 

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density                              = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                        = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature                          = 293.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                           = 2.38

    # The value of the thermal expansion coefficient $\beta$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient                  = 4e-5

    # The temperature dependence of viscosity. Dimensionless exponent.
    set Thermal viscosity exponent                     = 0.0

    # The value of the constant viscosity. Units: \si{\pascal\second}.
    set Viscosity                                      = 5e24

    # A list of prefactors for the viscosity for each phase. The reference
    # viscosity will be multiplied by this factor to get the corresponding
    # viscosity for each phase. List must have one more entry than Phase
    # transition depths. Units: non-dimensional.
    set Viscosity prefactors                           = 
  end

  subsection Latent heat melt
    # Constant parameter in the quadratic function that approximates the
    # solidus of peridotite. Units: \si{\degreeCelsius}.
    set A1                                             = 1085.7

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the solidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal}.
    set A2                                             = 1.329e-7

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the solidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set A3                                             = -5.1e-18

    # Constant parameter in the quadratic function that approximates the
    # lherzolite liquidus used for calculating the fraction of
    # peridotite-derived melt. Units: \si{\degreeCelsius}.
    set B1                                             = 1475.0

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the  lherzolite liquidus used for calculating the fraction
    # of peridotite-derived melt. Units: \si{\degreeCelsius\per\pascal}.
    set B2                                             = 8.0e-8

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the  lherzolite liquidus used for calculating the fraction
    # of peridotite-derived melt. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set B3                                             = -3.2e-18

    # Constant parameter in the quadratic function that approximates the
    # liquidus of peridotite. Units: \si{\degreeCelsius}.
    set C1                                             = 1780.0

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the liquidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal}.
    set C2                                             = 4.50e-8

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the liquidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set C3                                             = -2.0e-18

    # A linear dependency of viscosity on composition. Dimensionless
    # prefactor.
    set Composition viscosity prefactor                = 1.0

    # The value of the compressibility $\kappa$. Units: \si{\per\pascal}.
    set Compressibility                                = 5.124e-12

    # Constant parameter in the quadratic function that approximates the
    # solidus of pyroxenite. Units: \si{\degreeCelsius}.
    set D1                                             = 976.0

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the solidus of pyroxenite. Note that this factor is
    # different from the value given in Sobolev, 2011, because they use the
    # potential temperature whereas we use the absolute temperature. Units:
    # \si{\degreeCelsius\per\pascal}.
    set D2                                             = 1.329e-7

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the solidus of pyroxenite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set D3                                             = -5.1e-18

    # If compositional fields are used, then one would frequently want to make
    # the density depend on these fields. In this simple material model, we
    # make the following assumptions: if no compositional fields are used in
    # the current simulation, then the density is simply the usual one with
    # its linear dependence on the temperature. If there are compositional
    # fields, then the density only depends on the first one in such a way
    # that the density has an additional term of the kind $+\Delta \rho \;
    # c_1(\mathbf x)$. This parameter describes the value of $\Delta \rho$.
    # Units: \si{\kilogram\per\meter\cubed}/unit change in composition.
    set Density differential for compositional field 1 = 0.

    # Prefactor of the linear depletion term in the quadratic function that
    # approximates the melt fraction of pyroxenite. Units:
    # \si{\degreeCelsius\per\pascal}.
    set E1                                             = 663.8

    # Prefactor of the quadratic depletion term in the quadratic function that
    # approximates the melt fraction of pyroxenite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set E2                                             = -611.4

    # Mass fraction of clinopyroxene in the peridotite to be molten. Units:
    # non-dimensional.
    set Mass fraction cpx                              = 0.15

    # Maximum melt fraction of pyroxenite in this parameterization. At higher
    # temperatures peridotite begins to melt.
    set Maximum pyroxenite melt fraction               = 0.5429

    # The entropy change for the phase transition from solid to melt of
    # peridotite. Units: \si{\joule\per\kelvin\per\kilogram}.
    set Peridotite melting entropy change              = -300.

    # The entropy change for the phase transition from solid to melt of
    # pyroxenite. Units: \si{\joule\per\kelvin\per\kilogram}.
    set Pyroxenite melting entropy change              = -400.

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density                              = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                        = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature                          = 293.

    # The relative density of melt compared to the solid material. This means,
    # the density change upon melting is this parameter times the density of
    # solid material.Units: non-dimensional.
    set Relative density of melt                       = 0.9

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                           = 2.38

    # The value of the thermal expansion coefficient $\alpha_s$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient                  = 4e-5

    # The value of the thermal expansion coefficient $\alpha_f$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient of melt          = 6.8e-5

    # The temperature dependence of viscosity. Dimensionless exponent.
    set Thermal viscosity exponent                     = 0.0

    # The value of the constant viscosity. Units: \si{\pascal\second}.
    set Viscosity                                      = 5e24

    # Exponent of the melting temperature in the melt fraction calculation.
    # Units: non-dimensional.
    set beta                                           = 1.5

    # Constant in the linear function that approximates the clinopyroxene
    # reaction coefficient. Units: non-dimensional.
    set r1                                             = 0.5

    # Prefactor of the linear pressure term in the linear function that
    # approximates the clinopyroxene reaction coefficient. Units:
    # \si{\per\pascal}.
    set r2                                             = 8e-11
  end

  subsection Melt global
    # The density contrast between material with a depletion of 1 and a
    # depletion of zero. Negative values indicate lower densities of depleted
    # material. Depletion is indicated by the compositional field with the
    # name peridotite. Not used if this field does not exist in the model.
    # Units: \si{\kilogram\per\meter\cubed}.
    set Depletion density change                   = 0.0

    # The solidus temperature change for a depletion of 100\%. For positive
    # values, the solidus gets increased for a positive peridotite field
    # (depletion) and lowered for a negative peridotite field (enrichment).
    # Scaling with depletion is linear. Only active when fractional melting is
    # used. Units: \si{\kelvin}.
    set Depletion solidus change                   = 200.0

    # $\alpha_F$: exponential dependency of viscosity on the depletion field
    # $F$ (called peridotite). Dimensionless factor. With a value of 0.0 (the
    # default) the viscosity does not depend on the depletion. The effective
    # viscosity increasedue to depletion is defined as $exp( \alpha_F * F)$.
    # Rationale: melting dehydrates the source rock by removing most of the
    # volatiles,and makes it stronger. Hirth and Kohlstedt (1996) report
    # typical values around a factor 100 to 1000 viscosity contrast between
    # wet and dry rocks, although some experimental studies report a smaller
    # (factor 10) contrast (e.g. Fei et al., 2013).
    set Exponential depletion strengthening factor = 0.0

    # The porosity dependence of the viscosity. Units: dimensionless.
    set Exponential melt weakening factor          = 27.

    # Whether to include melting and freezing (according to a simplified
    # linear melting approximation in the model (if true), or not (if false).
    set Include melting and freezing               = true

    # $\Delta \eta_{F,max}$: maximum depletion strengthening of viscosity.
    # Rationale: melting dehydrates the source rock by removing most of the
    # volatiles,and makes it stronger. Hirth and Kohlstedt (1996) report
    # typical values around a factor 100 to 1000 viscosity contrast between
    # wet and dry rocks, although some experimental studies report a smaller
    # (factor 10) contrast (e.g. Fei et al., 2013).
    set Maximum Depletion viscosity change         = 1.0e3

    # The value of the pressure derivative of the melt bulk modulus. Units:
    # None.
    set Melt bulk modulus derivative               = 0.0

    # The value of the compressibility of the melt. Units: \si{\per\pascal}.
    set Melt compressibility                       = 0.0

    # In case the operator splitting scheme is used, the porosity field can
    # not be set to a new equilibrium melt fraction instantly, but the model
    # has to provide a melting time scale instead. This time scale defines how
    # fast melting happens, or more specifically, the parameter defines the
    # time after which the deviation of the porosity from the equilibrium melt
    # fraction will be reduced to a fraction of $1/e$. So if the melting time
    # scale is small compared to the time step size, the reaction will be so
    # fast that the porosity is very close to the equilibrium melt fraction
    # after reactions are computed. Conversely, if the melting time scale is
    # large compared to the time step size, almost no melting and freezing
    # will occur.
    # 
    # Also note that the melting time scale has to be larger than or equal to
    # the reaction time step used in the operator splitting scheme, otherwise
    # reactions can not be computed. If the model does not use operator
    # splitting, this parameter is not used. Units: yr or s, depending on the
    # ``Use years in output instead of seconds'' parameter.
    set Melting time scale for operator splitting  = 1e3

    # The linear solidus temperature change with pressure. For positive
    # values, the solidus gets increased for positive pressures. Units:
    # \si{\per\pascal}.
    set Pressure solidus change                    = 6e-8

    # The value of the constant bulk viscosity $\xi_0$ of the solid matrix.
    # This viscosity may be modified by both temperature and porosity
    # dependencies. Units: \si{\pascal\second}.
    set Reference bulk viscosity                   = 1e22

    # Reference density of the melt/fluid$\rho_{f,0}$. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference melt density                     = 2500.

    # The value of the constant melt viscosity $\eta_f$. Units:
    # \si{\pascal\second}.
    set Reference melt viscosity                   = 10.

    # Reference permeability of the solid host rock.Units:
    # \si{\meter\squared}.
    set Reference permeability                     = 1e-8

    # The value of the constant viscosity $\eta_0$ of the solid matrix. This
    # viscosity may be modified by both temperature and porosity dependencies.
    # Units: \si{\pascal\second}.
    set Reference shear viscosity                  = 5e20

    # Reference density of the solid $\rho_{s,0}$. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference solid density                    = 3000.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                    = 1250.

    # The reference temperature $T_0$. The reference temperature is used in
    # both the density and viscosity formulas. Units: \si{\kelvin}.
    set Reference temperature                      = 293.

    # The value of the compressibility of the solid matrix. Units:
    # \si{\per\pascal}.
    set Solid compressibility                      = 0.0

    # Solidus for a pressure of zero. Units: \si{\kelvin}.
    set Surface solidus                            = 1300.

    # The temperature dependence of the bulk viscosity. Dimensionless
    # exponent. See the general documentation of this model for a formula that
    # states the dependence of the viscosity on this factor, which is called
    # $\beta$ there.
    set Thermal bulk viscosity exponent            = 0.0

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                       = 4.7

    # The value of the thermal expansion coefficient $\beta$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient              = 2e-5

    # The temperature dependence of the shear viscosity. Dimensionless
    # exponent. See the general documentation of this model for a formula that
    # states the dependence of the viscosity on this factor, which is called
    # $\beta$ there.
    set Thermal viscosity exponent                 = 0.0
  end

  subsection Melt simple
    # Constant parameter in the quadratic function that approximates the
    # solidus of peridotite. Units: \si{\degreeCelsius}.
    set A1                                        = 1085.7

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the solidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal}.
    set A2                                        = 1.329e-7

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the solidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set A3                                        = -5.1e-18

    # Constant parameter in the quadratic function that approximates the
    # lherzolite liquidus used for calculating the fraction of
    # peridotite-derived melt. Units: \si{\degreeCelsius}.
    set B1                                        = 1475.0

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the  lherzolite liquidus used for calculating the fraction
    # of peridotite-derived melt. Units: \si{\degreeCelsius\per\pascal}.
    set B2                                        = 8.0e-8

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the  lherzolite liquidus used for calculating the fraction
    # of peridotite-derived melt. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set B3                                        = -3.2e-18

    # Constant parameter in the quadratic function that approximates the
    # liquidus of peridotite. Units: \si{\degreeCelsius}.
    set C1                                        = 1780.0

    # Prefactor of the linear pressure term in the quadratic function that
    # approximates the liquidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal}.
    set C2                                        = 4.50e-8

    # Prefactor of the quadratic pressure term in the quadratic function that
    # approximates the liquidus of peridotite. Units:
    # \si{\degreeCelsius\per\pascal\squared}.
    set C3                                        = -2.0e-18

    # The density contrast between material with a depletion of 1 and a
    # depletion of zero. Negative values indicate lower densities of depleted
    # material. Depletion is indicated by the compositional field with the
    # name peridotite. Not used if this field does not exist in the model.
    # Units: \si{\kilogram\per\meter\cubed}.
    set Depletion density change                  = 0.0

    # The solidus temperature change for a depletion of 100\%. For positive
    # values, the solidus gets increased for a positive peridotite field
    # (depletion) and lowered for a negative peridotite field (enrichment).
    # Scaling with depletion is linear. Only active when fractional melting is
    # used. Units: \si{\kelvin}.
    set Depletion solidus change                  = 200.0

    # The porosity dependence of the viscosity. Units: dimensionless.
    set Exponential melt weakening factor         = 27.

    # Freezing rate of melt when in subsolidus regions. If this parameter is
    # set to a number larger than 0.0, it specifies the fraction of melt that
    # will freeze per year (or per second, depending on the ``Use years in
    # output instead of seconds'' parameter), as soon as the porosity exceeds
    # the equilibrium melt fraction, and the equilibrium melt fraction falls
    # below the depletion. In this case, melt will freeze according to the
    # given rate until one of those conditions is not fulfilled anymore. The
    # reasoning behind this is that there should not be more melt present than
    # the equilibrium melt fraction, as melt production decreases with
    # increasing depletion, but the freezing process of melt also reduces the
    # depletion by the same amount, and as soon as the depletion falls below
    # the equilibrium melt fraction, we expect that material should melt again
    # (no matter how much melt is present). This is quite a simplification and
    # not a realistic freezing parameterization, but without tracking the melt
    # composition, there is no way to compute freezing rates accurately. If
    # this parameter is set to zero, no freezing will occur. Note that
    # freezing can never be faster than determined by the ``Melting time scale
    # for operator splitting''. The product of the ``Freezing rate'' and the
    # ``Melting time scale for operator splitting'' defines how fast freezing
    # occurs with respect to melting (if the product is 0.5, melting will
    # occur twice as fast as freezing). Units: 1/yr or 1/s, depending on the
    # ``Use years in output instead of seconds'' parameter.
    set Freezing rate                             = 0.0

    # Mass fraction of clinopyroxene in the peridotite to be molten. Units:
    # non-dimensional.
    set Mass fraction cpx                         = 0.15

    # The value of the pressure derivative of the melt bulk modulus. Units:
    # None.
    set Melt bulk modulus derivative              = 0.0

    # The value of the compressibility of the melt. Units: \si{\per\pascal}.
    set Melt compressibility                      = 0.0

    # Depth above that melt will be extracted from the model, which is done by
    # a negative reaction term proportional to the porosity field. Units:
    # \si{\meter}.
    set Melt extraction depth                     = 1000.0

    # Because the operator splitting scheme is used, the porosity field can
    # not be set to a new equilibrium melt fraction instantly, but the model
    # has to provide a melting time scale instead. This time scale defines how
    # fast melting happens, or more specifically, the parameter defines the
    # time after which the deviation of the porosity from the equilibrium melt
    # fraction will be reduced to a fraction of $1/e$. So if the melting time
    # scale is small compared to the time step size, the reaction will be so
    # fast that the porosity is very close to the equilibrium melt fraction
    # after reactions are computed. Conversely, if the melting time scale is
    # large compared to the time step size, almost no melting and freezing
    # will occur.
    # 
    # Also note that the melting time scale has to be larger than or equal to
    # the reaction time step used in the operator splitting scheme, otherwise
    # reactions can not be computed. Units: yr or s, depending on the ``Use
    # years in output instead of seconds'' parameter.
    set Melting time scale for operator splitting = 1e3

    # The entropy change for the phase transition from solid to melt of
    # peridotite. Units: \si{\joule\per\kelvin\per\kilogram}.
    set Peridotite melting entropy change         = -300.

    # The value of the constant bulk viscosity $\xi_0$ of the solid matrix.
    # This viscosity may be modified by both temperature and porosity
    # dependencies. Units: \si{\pascal\second}.
    set Reference bulk viscosity                  = 1e22

    # Reference density of the melt/fluid$\rho_{f,0}$. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference melt density                    = 2500.

    # The value of the constant melt viscosity $\eta_f$. Units:
    # \si{\pascal\second}.
    set Reference melt viscosity                  = 10.

    # Reference permeability of the solid host rock.Units:
    # \si{\meter\squared}.
    set Reference permeability                    = 1e-8

    # The value of the constant viscosity $\eta_0$ of the solid matrix. This
    # viscosity may be modified by both temperature and porosity dependencies.
    # Units: \si{\pascal\second}.
    set Reference shear viscosity                 = 5e20

    # Reference density of the solid $\rho_{s,0}$. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference solid density                   = 3000.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                   = 1250.

    # The reference temperature $T_0$. The reference temperature is used in
    # both the density and viscosity formulas. Units: \si{\kelvin}.
    set Reference temperature                     = 293.

    # The value of the compressibility of the solid matrix. Units:
    # \si{\per\pascal}.
    set Solid compressibility                     = 0.0

    # The temperature dependence of the bulk viscosity. Dimensionless
    # exponent. See the general documentation of this model for a formula that
    # states the dependence of the viscosity on this factor, which is called
    # $\beta$ there.
    set Thermal bulk viscosity exponent           = 0.0

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                      = 4.7

    # The value of the thermal expansion coefficient $\beta$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient             = 2e-5

    # The temperature dependence of the shear viscosity. Dimensionless
    # exponent. See the general documentation of this model for a formula that
    # states the dependence of the viscosity on this factor, which is called
    # $\beta$ there.
    set Thermal viscosity exponent                = 0.0

    # If fractional melting should be used (if true), including a solidus
    # change based on depletion (in this case, the amount of melt that has
    # migrated away from its origin), and freezing of melt when it has moved
    # to a region with temperatures lower than the solidus; or if batch
    # melting should be used (if false), assuming that the melt fraction only
    # depends on temperature and pressure, and how much melt has already been
    # generated at a given point, but not considering movement of melt in the
    # melting parameterization.
    # 
    # Note that melt does not freeze unless the 'Freezing rate' parameter is
    # set to a value larger than 0.
    set Use fractional melting                    = false

    # If the compressibility should be used everywhere in the code (if true),
    # changing the volume of material when the density changes, or only in the
    # momentum conservation and advection equations (if false).
    set Use full compressibility                  = false

    # Exponent of the melting temperature in the melt fraction calculation.
    # Units: non-dimensional.
    set beta                                      = 1.5

    # Constant in the linear function that approximates the clinopyroxene
    # reaction coefficient. Units: non-dimensional.
    set r1                                        = 0.5

    # Prefactor of the linear pressure term in the linear function that
    # approximates the clinopyroxene reaction coefficient. Units:
    # \si{\per\pascal}.
    set r2                                        = 8e-11
  end

  subsection Modified Tait model
    # The Einstein temperature at the reference pressure and temperature.
    # Units: \si{\kelvin}.
    set Einstein temperature              = 600.

    # The value of the first pressure derivative of the isothermal bulk
    # modulus at the reference pressure and temperature. Units: None.
    set Reference bulk modulus derivative = 4.

    # The density at the reference pressure and temperature. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference density                 = 3300.

    # The isothermal bulk modulus at the reference pressure and temperature.
    # Units: \si{\pascal}.
    set Reference isothermal bulk modulus = 125e9

    # Reference pressure $P_0$. Units: \si{\pascal}.
    set Reference pressure                = 1e5

    # Reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature             = 298.15

    # The thermal expansion coefficient at the reference pressure and
    # temperature. Units: \si{\per\kelvin}.
    set Reference thermal expansivity     = 2e-5

    # The value of the constant thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity              = 4.7

    # The value of the constant viscosity $\eta_0$. Units:
    # \si{\pascal\second}.
    set Viscosity                         = 1e21


    subsection Reference heat capacity function
      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants  = 
      set Function expression = 1.25e3

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names      = x,t
    end

  end

  subsection Multicomponent
    # List of densities for background mantle and compositional fields,for a
    # total of N+M+1 values, where N is the number of compositional fields and
    # M is the number of phases. If only one value is given, then all use the
    # same value. Units: \si{\kilogram\per\meter\cubed}.
    set Densities                  = 3300.

    # List of specific heats $C_p$ for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Heat capacities            = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature      = 293.

    # List of thermal conductivities for background mantle and compositional
    # fields,for a total of N+1 values, where N is the number of compositional
    # fields.If only one value is given, then all use the same value. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivities     = 4.7

    # List of thermal expansivities for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units: \si{\per\kelvin}.
    set Thermal expansivities      = 0.000040

    # List of viscosities for background mantle and compositional fields,for a
    # total of N+1 values, where N is the number of compositional fields.If
    # only one value is given, then all use the same value. Units:
    # \si{\pascal\second}.
    set Viscosities                = 1.e21

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme = harmonic
  end

  subsection Multicomponent compressible
    # List of isochoric specific heats $C_v$ for background mantle and
    # compositional fields,for a total of N+1 values, where N is the number of
    # compositional fields.If only one value is given, then all use the same
    # value. Units: \si{\joule\per\kelvin\per\kilogram}.
    set Isochoric specific heats                     = 1250.

    # List of isothermal pressure derivatives of the bulk moduli for
    # background mantle and compositional fields,for a total of N+1 values,
    # where N is the number of compositional fields.If only one value is
    # given, then all use the same value. Units: [].
    set Isothermal bulk modulus pressure derivatives = 4.

    # List of densities for background mantle and compositional fields,for a
    # total of N+1 values, where N is the number of compositional fields.If
    # only one value is given, then all use the same value. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Reference densities                          = 3300.

    # List of isothermal compressibilities for background mantle and
    # compositional fields,for a total of N+1 values, where N is the number of
    # compositional fields.If only one value is given, then all use the same
    # value. Units: \si{\per\pascal}.
    set Reference isothermal compressibilities       = 4e-12

    # List of reference temperatures $T_0$ for background mantle and
    # compositional fields,for a total of N+1 values, where N is the number of
    # compositional fields.If only one value is given, then all use the same
    # value. Units: \si{\kelvin}.
    set Reference temperatures                       = 298.15

    # List of thermal expansivities for background mantle and compositional
    # fields,for a total of N+1 values, where N is the number of compositional
    # fields.If only one value is given, then all use the same value. Units:
    # \si{\per\kelvin}.
    set Reference thermal expansivities              = 4.e-5

    # List of thermal conductivities for background mantle and compositional
    # fields,for a total of N+1 values, where N is the number of compositional
    # fields.If only one value is given, then all use the same value. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivities                       = 4.7

    # List of viscosities for background mantle and compositional fields,for a
    # total of N+1 values, where N is the number of compositional fields.If
    # only one value is given, then all use the same value. Units:
    # \si{\pascal\second}.
    set Viscosities                                  = 1.e21

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme                   = harmonic
  end

  subsection Nondimensional model
    # Dissipation number. Pick 0.0 for incompressible computations.
    set Di                              = 0.0

    # Rayleigh number Ra
    set Ra                              = 1e4

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density               = 1.0

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat         = 1.0

    # Whether to use the TALA instead of the ALA approximation.
    set Use TALA                        = false

    # Exponential depth prefactor for viscosity.
    set Viscosity depth prefactor       = 0.0

    # Exponential temperature prefactor for viscosity.
    set Viscosity temperature prefactor = 0.0

    # Grueneisen parameter
    set gamma                           = 1.0
  end

  subsection PerpleX lookup model
    # The value of the maximum pressure used to query PerpleX. Units:
    # \si{\pascal}.
    set Maximum material pressure    = 1.e12

    # The value of the maximum temperature used to query PerpleX. Units:
    # \si{\kelvin}.
    set Maximum material temperature = 6000.

    # The value of the minimum pressure used to query PerpleX. Units:
    # \si{\pascal}.
    set Minimum material pressure    = 1.e5

    # The value of the minimum temperature used to query PerpleX. Units:
    # \si{\kelvin}.
    set Minimum material temperature = 0.

    # The name of the PerpleX input file (should end with .dat).
    set PerpleX input file name      = rock.dat

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity         = 4.7

    # The value of the viscosity $\eta$. Units: \si{\pascal\second}.
    set Viscosity                    = 5e24
  end

  subsection Replace lithosphere viscosity
    # The name of a material model that will be modified by a replacingthe
    # viscosity in the lithosphere by a constant value. Valid values for this
    # parameter are the names of models that are also valid for the ``Material
    # models/Model name'' parameter. See the documentation for more
    # information.
    set Base model                 = simple

    # The path to the LAB depth data file
    set Data directory             = $ASPECT_SOURCE_DIR/data/initial-temperature/lithosphere-mask/

    # Method that is used to specify the depth of the
    # lithosphere-asthenosphere boundary.
    set Depth specification method = Value

    # File from which the lithosphere-asthenosphere boundary depth data is
    # read.
    set LAB depth filename         = LAB_CAM2016.txt

    # The viscosity within lithosphere, applied abovethe maximum lithosphere
    # depth.
    set Lithosphere viscosity      = 1e23

    # Units: \si{\meter}.The maximum depth of the lithosphere. The model will
    # be NaNs below this depth.
    set Maximum lithosphere depth  = 200000.0
  end

  subsection Simple compressible model
    # The value of the reference compressibility. Units: \si{\per\pascal}.
    set Reference compressibility     = 4e-12

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density             = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat       = 1250.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity          = 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient = 2e-5

    # The value of the viscosity $\eta$. Units: \si{\pascal\second}.
    set Viscosity                     = 1000000000000000000000.000000
  end

  subsection Simple model
    # A linear dependency of viscosity on the first compositional field.
    # Dimensionless prefactor. With a value of 1.0 (the default) the viscosity
    # does not depend on the composition. See the general documentation of
    # this model for a formula that states the dependence of the viscosity on
    # this factor, which is called $\xi$ there.
    set Composition viscosity prefactor                = 1.0

    # If compositional fields are used, then one would frequently want to make
    # the density depend on these fields. In this simple material model, we
    # make the following assumptions: if no compositional fields are used in
    # the current simulation, then the density is simply the usual one with
    # its linear dependence on the temperature. If there are compositional
    # fields, then the material model determines how many of them influence
    # the density. The composition-dependence adds a term of the kind $+\Delta
    # \rho \; c_1(\mathbf x)$. This parameter describes the value of $\Delta
    # \rho$. Units: \si{\kilogram\per\meter\cubed}/unit change in
    # composition.
    set Density differential for compositional field 1 = 0.

    # The maximum value of the viscosity prefactor associated with temperature
    # dependence.
    set Maximum thermal prefactor                      = 1.0e2

    # The minimum value of the viscosity prefactor associated with temperature
    # dependence.
    set Minimum thermal prefactor                      = 1.0e-2

    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density                              = 3300.0 # default: 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat                        = 1250.0 # default: 1250.

    # The reference temperature $T_0$. The reference temperature is used in
    # both the density and viscosity formulas. Units: \si{\kelvin}.
    set Reference temperature                          = 293.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                           = 3.0    # default: 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient                  = 0.0    # default: 2e-5

    # The temperature dependence of viscosity. Dimensionless exponent. See the
    # general documentation of this model for a formula that states the
    # dependence of the viscosity on this factor, which is called $\beta$
    # there.
    set Thermal viscosity exponent                     = 0.0

    # The value of the constant viscosity $\eta_0$. This viscosity may be
    # modified by both temperature and compositional dependencies. Units:
    # \si{\pascal\second}.
    set Viscosity                                      = 1e21   # default: 5e24
  end

  subsection Simpler model
    # Reference density $\rho_0$. Units: \si{\kilogram\per\meter\cubed}.
    set Reference density             = 3300.

    # The value of the specific heat $C_p$. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Reference specific heat       = 1250.

    # The reference temperature $T_0$. The reference temperature is used in
    # both the density and viscosity formulas. Units: \si{\kelvin}.
    set Reference temperature         = 293.

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity          = 4.7

    # The value of the thermal expansion coefficient $\alpha$. Units:
    # \si{\per\kelvin}.
    set Thermal expansion coefficient = 2e-5

    # The value of the viscosity $\eta$. Units: \si{\pascal\second}.
    set Viscosity                     = 5000000000000000452984832.000000
  end

  subsection Steinberger model
    # Whether to use bilinear interpolation to compute material properties
    # (slower but more accurate).
    set Bilinear interpolation                        = true

    # The path to the model data. The path may also include the special text
    # '$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory                                = $ASPECT_SOURCE_DIR/data/material-model/steinberger/

    # Whether to include latent heat effects in the calculation of thermal
    # expansivity and specific heat. Following the approach of Nakagawa et al.
    # 2009.
    set Latent heat                                   = false

    # The file name of the lateral viscosity data.
    set Lateral viscosity file name                   = temp-viscosity-prefactor.txt

    # The file names of the material data (material data is assumed to be in
    # order with the ordering of the compositional fields). Note that there
    # are three options on how many files need to be listed here: 1. If only
    # one file is provided, it is used for the whole model domain, and
    # compositional fields are ignored. 2. If there is one more file name than
    # the number of compositional fields, then the first file is assumed to
    # define a `background composition' that is modified by the compositional
    # fields. If there are exactly as many files as compositional fields, the
    # fields are assumed to represent the mass fractions of different
    # materials and the average property is computed as a sum of the value of
    # the compositional field times the material property of that field.
    set Material file names                           = pyr-ringwood88.txt

    # The relative cutoff value for lateral viscosity variations caused by
    # temperature deviations. The viscosity may vary laterally by this factor
    # squared.
    set Maximum lateral viscosity variation           = 1e2

    # The maximum viscosity that is allowed in the viscosity calculation.
    # Larger values will be cut off.
    set Maximum viscosity                             = 1e23

    # The minimum viscosity that is allowed in the viscosity calculation.
    # Smaller values will be cut off.
    set Minimum viscosity                             = 1e19

    # Number of bands to compute laterally averaged temperature within.
    set Number lateral average bands                  = 10

    # The file name of the radial viscosity data.
    set Radial viscosity file name                    = radial-visc.txt

    # The reference viscosity that is used for pressure scaling. To understand
    # how pressure scaling works, take a look at \cite{KHB12}. In particular,
    # the value of this parameter would not affect the solution computed by
    # \aspect{} if we could do arithmetic exactly; however, computers do
    # arithmetic in finite precision, and consequently we need to scale
    # quantities in ways so that their magnitudes are roughly the same. As
    # explained in \cite{KHB12}, we scale the pressure during some
    # computations (never visible by users) by a factor that involves a
    # reference viscosity. This parameter describes this reference viscosity.
    # 
    # For problems with a constant viscosity, you will generally want to
    # choose the reference viscosity equal to the actual viscosity. For
    # problems with a variable viscosity, the reference viscosity should be a
    # value that adequately represents the order of magnitude of the
    # viscosities that appear, such as an average value or the value one would
    # use to compute a Rayleigh number.
    # 
    # Units: \si{\pascal\second}.
    set Reference viscosity                           = 1e23

    # The value of the thermal conductivity $k$. Units:
    # \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivity                          = 4.7

    # Whether to use to use the laterally averaged temperature instead of the
    # adiabatic temperature as reference for the viscosity calculation. This
    # ensures that the laterally averaged viscosities remain more or less
    # constant over the model runtime. This behaviour might or might not be
    # desired.
    set Use lateral average temperature for viscosity = true
  end

  subsection Visco Plastic
    # List of activation energies, $E$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\joule\per\mole}.
    set Activation energies for Peierls creep              = 320e3

    # List of activation energies, $E_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\joule\per\mole}.
    set Activation energies for diffusion creep            = 375e3

    # List of activation energies, $E_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\joule\per\mole}.
    set Activation energies for dislocation creep          = 530e3

    # List of activation volumes, $V$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\meter\cubed\per\mole}.
    set Activation volumes for Peierls creep               = 1.4e-5

    # List of activation volumes, $V_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\meter\cubed\per\mole}.
    set Activation volumes for diffusion creep             = 6e-6

    # List of activation volumes, $V_a$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\meter\cubed\per\mole}.
    set Activation volumes for dislocation creep           = 1.4e-5

    # Add an adiabatic temperature gradient to the temperature used in the
    # flow law so that the activation volume is consistent with what one would
    # use in a earth-like (compressible) model. Default is set so this is off.
    # Note that this is a linear approximation of the real adiabatic gradient,
    # which is okay for the upper mantle, but is not really accurate for the
    # lower mantle. Using a pressure gradient of 32436 Pa/m, then a value of
    # 0.3 K/km = 0.0003 K/m = 9.24e-09 K/Pa gives an earth-like adiabat.Units:
    # \si{\kelvin\per\pascal}.
    set Adiabat temperature gradient for viscosity         = 0.0

    # Whether to allow negative pressures to be used in the computation of
    # plastic yield stresses and viscosities. Setting this parameter to true
    # may be advantageous in models without gravity where the dynamic stresses
    # are much higher than the lithostatic pressure. If false, the minimum
    # pressure in the plasticity formulation will be set to zero.
    set Allow negative pressures in plasticity             = false

    # List of angles of internal friction, $\phi$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. For a value of zero, in 2D the von Mises
    # criterion is retrieved. Angles higher than 30 degrees are harder to
    # solve numerically. Units: degrees.
    set Angles of internal friction                        = 0.

    # List of cohesion strain weakening factors for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value.  Units: None.
    set Cohesion strain weakening factors                  = 1.

    # List of cohesions, $C$, for background material and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. The extremely large default cohesion value (1e20
    # Pa) prevents the viscous stress from exceeding the yield stress. Units:
    # \si{\pascal}.
    set Cohesions                                          = 1e20

    # List of constant viscosity prefactors (i.e., multiplicative factors) for
    # background material and compositional fields, for a total of N+1 where N
    # is the number of compositional fields. Units: none.
    set Constant viscosity prefactors                      = 1.0

    # Whether to directly define thermal conductivities for each compositional
    # field instead of calculating the values through the specified thermal
    # diffusivities, densities, and heat capacities.
    set Define thermal conductivities                      = false

    # Whether to list phase transitions by depth or pressure. If this
    # parameter is true, then the input file will use Phase transitions depths
    # and Phase transition widths to define the phase transition. If it is
    # false, the parameter file will read in phase transition data from Phase
    # transition pressures and Phase transition pressure widths.
    set Define transition by depth instead of pressure     = true

    # List of densities for background mantle and compositional fields,for a
    # total of N+M+1 values, where N is the number of compositional fields and
    # M is the number of phases. If only one value is given, then all use the
    # same value. Units: \si{\kilogram\per\meter\cubed}.
    set Densities                                          = 3300.

    # List of elastic shear moduli, $G$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. The default value of 75 GPa is representative
    # of mantle rocks. Units: Pa.
    set Elastic shear moduli                               = 75.0e9

    # List of strain weakening interval final strains for the cohesion and
    # friction angle parameters of the background material and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value.  Units: None.
    set End plasticity strain weakening intervals          = 1.

    # List of strain weakening interval final strains for the diffusion and
    # dislocation prefactor parameters of the background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value.  Units: None.
    set End prefactor strain weakening intervals           = 1.

    # The fixed elastic time step $dte$. Units: years if the 'Use years in
    # output instead of seconds' parameter is set; seconds otherwise.
    set Fixed elastic time step                            = 1.e3

    # List of friction strain weakening factors for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value.  Units: None.
    set Friction strain weakening factors                  = 1.

    # Units: \si{\meter}.
    set Grain size                                         = 1e-3

    # List of grain size exponents, $m_{\text{diffusion}}$, for background
    # material and compositional fields, for a total of N+1 values, where N is
    # the number of compositional fields. If only one value is given, then all
    # use the same value. Units: None.
    set Grain size exponents for diffusion creep           = 3.

    # List of specific heats $C_p$ for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Heat capacities                                    = 1250.

    # Whether to include Peierls creep in the rheological formulation.
    set Include Peierls creep                              = false

    # Whether to include elastic effects in the rheological formulation.
    set Include viscoelasticity                            = false

    # Maximum number of iterations to find the correct Peierls strain rate.
    set Maximum Peierls strain rate iterations             = 40

    # Upper cutoff for effective viscosity. Units: \si{\pascal\second}.
    set Maximum viscosity                                  = 1e28

    # Limits the maximum value of the yield stress determined by the
    # Drucker-Prager plasticity parameters. Default value is chosen so this is
    # not automatically used. Values of 100e6--1000e6 $Pa$ have been used in
    # previous models. Units: \si{\pascal}.
    set Maximum yield stress                               = 1e12

    # Stabilizes strain dependent viscosity. Units: \si{\per\second}.
    set Minimum strain rate                                = 1.0e-20

    # Lower cutoff for effective viscosity. Units: \si{\pascal\second}.
    set Minimum viscosity                                  = 1e17

    # Select what type of Peierls creep flow law to use. Currently, the
    # available options are 'exact', which uses a Newton-Raphson iterative
    # method to find the stress and then compute viscosity, and 'viscosity
    # approximation', in which viscosity is an explicit function of the strain
    # rate invariant, rather than stress.
    set Peierls creep flow law                             = viscosity approximation

    # List of fitting parameters $\gamma$ between stress $\sigma$ and the
    # Peierls stress $\sigma_{\text{peierls}}$ for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: none
    set Peierls fitting parameters                         = 0.17

    # List of the first Peierls creep glide parameters, $p$, for background
    # and compositional fields for a total of N+1 values, where N is the
    # number of compositional fields. If only one value is given, then all use
    # the same value. Units: none
    set Peierls glide parameters p                         = 0.5

    # List of the second Peierls creep glide parameters, $q$, for background
    # and compositional fields for a total of N+1 values, where N is the
    # number of compositional fields. If only one value is given, then all use
    # the same value. Units: none
    set Peierls glide parameters q                         = 1.0

    # Tolerance for the iterative solve to find the correct Peierls creep
    # strain rate.
    set Peierls strain rate residual tolerance             = 1e-22

    # List of stress limits for Peierls creep $\sigma_{\text{peierls}}$ for
    # background material and compositional fields, for a total of N+1 values,
    # where N is the number of compositional fields. If only one value is
    # given, then all use the same value. Units: \si{\pascal}
    set Peierls stresses                                   = 5.e9

    # A list of Clapeyron slopes for each phase transition. A positive
    # Clapeyron slope indicates that the phase transition will occur in a
    # greater depth, if the temperature is higher than the one given in Phase
    # transition temperatures and in a smaller depth, if the temperature is
    # smaller than the one given in Phase transition temperatures. For
    # negative slopes the other way round. List must have the same number of
    # entries as Phase transition depths. Units: \si{\pascal\per\kelvin}.
    set Phase transition Clapeyron slopes                  = 

    # A list of depths where phase transitions occur. Values must
    # monotonically increase. Units: \si{\meter}.
    set Phase transition depths                            = 

    # A list of widths for each phase transition, in terms of pressure. The
    # phase functions are scaled with these values, leading to a jump between
    # phases for a value of zero and a gradual transition for larger values.
    # List must have the same number of entries as Phase transition pressures.
    # Define transition by depth instead of pressure must be set to false to
    # use this parameter. Units: \si{\pascal}.
    set Phase transition pressure widths                   = 

    # A list of pressures where phase transitions occur. Values must
    # monotonically increase. Define transition by depth instead of pressure
    # must be set to false to use this parameter. Units: \si{\pascal}.
    set Phase transition pressures                         = 

    # A list of temperatures where phase transitions occur. Higher or lower
    # temperatures lead to phase transition occurring in smaller or greater
    # depths than given in Phase transition depths, depending on the Clapeyron
    # slope given in Phase transition Clapeyron slopes. List must have the
    # same number of entries as Phase transition depths. Units: \si{\kelvin}.
    set Phase transition temperatures                      = 

    # A list of widths for each phase transition, in terms of depth. The phase
    # functions are scaled with these values, leading to a jump between phases
    # for a value of zero and a gradual transition for larger values. List
    # must have the same number of entries as Phase transition depths. Units:
    # \si{\meter}.
    set Phase transition widths                            = 

    # Viscosity of the damper that acts in parallel with the plastic viscosity
    # to produce mesh-independent behavior at sufficient resolutions. Units:
    # \si{\pascal\second}
    set Plastic damper viscosity                           = 0.0

    # List of viscous strain weakening factors for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value.  Units: None.
    set Prefactor strain weakening factors                 = 1.

    # A viscosity prefactor for the viscosity approximation, for a total of
    # N+1 values, where N is the number of compositional fields. If only one
    # value is given, then all use the same value.  Units: None
    set Prefactors for Frank Kamenetskii                   = 1.e21

    # List of viscosity prefactors, $A$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\pascal}$^{-n_{\text{peierls}}}$
    # \si{\per\second}
    set Prefactors for Peierls creep                       = 1.4e-19

    # List of viscosity prefactors, $A$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units:
    # \si{\per\pascal\meter}$^{m_{\text{diffusion}}}$\si{\per\second}.
    set Prefactors for diffusion creep                     = 1.5e-15

    # List of viscosity prefactors, $A$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\pascal}$^{-n_{\text{dislocation}}}$
    # \si{\per\second}.
    set Prefactors for dislocation creep                   = 1.1e-16

    # Reference strain rate for first time step. Units: \si{\per\second}.
    set Reference strain rate                              = 1.0e-15

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature                              = 293.

    # Reference viscosity for nondimensionalization. To understand how
    # pressure scaling works, take a look at \cite{KHB12}. In particular, the
    # value of this parameter would not affect the solution computed by
    # \aspect{} if we could do arithmetic exactly; however, computers do
    # arithmetic in finite precision, and consequently we need to scale
    # quantities in ways so that their magnitudes are roughly the same. As
    # explained in \cite{KHB12}, we scale the pressure during some
    # computations (never visible by users) by a factor that involves a
    # reference viscosity. This parameter describes this reference viscosity.
    # 
    # For problems with a constant viscosity, you will generally want to
    # choose the reference viscosity equal to the actual viscosity. For
    # problems with a variable viscosity, the reference viscosity should be a
    # value that adequately represents the order of magnitude of the
    # viscosities that appear, such as an average value or the value one would
    # use to compute a Rayleigh number.
    # 
    # Units: \si{\pascal\second}.
    set Reference viscosity                                = 1e22

    # List of strain weakening interval initial strains for the cohesion and
    # friction angle parameters of the background material and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value. Units: None.
    set Start plasticity strain weakening intervals        = 0.

    # List of strain weakening interval initial strains for the diffusion and
    # dislocation prefactor parameters of the background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value.  Units: None.
    set Start prefactor strain weakening intervals         = 0.

    # Whether to apply strain healing to plastic yielding and viscosity terms,
    # and if yes, which method to use. The following methods are available:
    # 
    # \item ``no healing'': No strain healing is applied.
    # 
    # \item ``temperature dependent'': Purely temperature dependent strain
    # healing applied to plastic yielding and viscosity terms, similar to the
    # temperature-dependent Frank Kamenetskii formulation, computes strain
    # healing as removing strain as a function of temperature, time, and a
    # user-defined healing rate and prefactor as done in Fuchs and Becker,
    # 2019, for mantle convection
    set Strain healing mechanism                           = no healing

    # Prefactor for temperature dependent strain healing. Units: None
    set Strain healing temperature dependent prefactor     = 15.

    # Recovery rate prefactor for temperature dependent strain healing. Units:
    # $1/s$
    set Strain healing temperature dependent recovery rate = 1.e-15

    # Whether to apply strain weakening to viscosity, cohesion and internal
    # angleof friction based on accumulated finite strain, and if yes, which
    # method to use. The following methods are available:
    # 
    # \item ``none'': No strain weakening is applied.
    # 
    # \item ``finite strain tensor'': The full finite strain tensor is
    # tracked, and its second invariant is used to weaken both the plastic
    # yield stress (specifically, the cohesion and friction angle) and the
    # pre-yield viscosity that arises from diffusion and/or dislocation creep.
    # 
    # \item ``total strain'': The finite strain is approximated as the product
    # of the second invariant of the strain rate in each time step and the
    # time step size, and this quantity is integrated and tracked over time.
    # It is used to weaken both the plastic yield stress (specifically, the
    # cohesion and friction angle) and the pre-yield viscosity.
    # 
    # \item ``plastic weakening with plastic strain only'': The finite strain
    # is approximated as the product of the second invariant of the strain
    # ratein each time step and the time step size in regions where material
    # is plastically yielding. This quantity is integrated and tracked over
    # time, and used to weaken the cohesion and friction angle. The pre-yield
    # viscosity is not weakened.
    # 
    # \item ``plastic weakening with total strain only'': The finite strain is
    # approximated as the product of the second invariant of the strain rate
    # in each time step and the time step size, and this quantity is
    # integrated and tracked over time. It is used to weaken the plastic yield
    # stress (specifically, the cohesion and internal friction angle). The
    # pre-yield viscosity is not weakened.
    # 
    # \item ``plastic weakening with plastic strain and viscous weakening with
    # viscous strain'': Both the finite strain accumulated by plastic
    # deformation and by viscous deformation are computed separately (each
    # approximated as the product of the second invariant of the corresponding
    # strain rate in each time step and the time step size). The plastic
    # strain is used to weaken the plastic yield stress (specifically, the
    # cohesion and yield angle), and the viscous strain is used to weaken the
    # pre-yield viscosity.
    # 
    # \item ``viscous weakening with viscous strain only'': The finite strain
    # is approximated as the product of the second invariant of the strain
    # rate in each time step and the time step size in regions where material
    # is not plastically yielding. This quantity is integrated and tracked
    # over time, and used to weaken the the pre-yield viscosity. The cohesion
    # and friction angle are not weakened.
    # 
    # \item ``default'': The default option has the same behavior as ``none'',
    # but is there to make sure that the original parameters for specifying
    # the strain weakening mechanism (``Use plastic/viscous strain
    # weakening'') are still allowed, but to guarantee that one uses either
    # the old parameter names or the new ones, never both.
    # 
    # If a compositional field named 'noninitial\_plastic\_strain' is included
    # in the parameter file, this field will automatically be excluded from
    # from volume fraction calculation and track the cumulative plastic strain
    # with the initial plastic strain values removed.
    set Strain weakening mechanism                         = default

    # List of stress exponents, $n_{\text{peierls}}$, for background material
    # and compositional fields, for a total of N+1 values, where N is the
    # number of compositional fields. If only one value is given, then all use
    # the same value.  Units: None.
    set Stress exponents for Peierls creep                 = 2.0

    # List of stress exponents, $n_{\text{diffusion}}$, for background mantle
    # and compositional fields, for a total of N+1 values, where N is the
    # number of compositional fields. The stress exponent for diffusion creep
    # is almost always equal to one. If only one value is given, then all use
    # the same value.  Units: None.
    set Stress exponents for diffusion creep               = 1.

    # List of stress exponents, $n_{\text{dislocation}}$, for background
    # material and compositional fields, for a total of N+1 values, where N is
    # the number of compositional fields. If only one value is given, then all
    # use the same value.  Units: None.
    set Stress exponents for dislocation creep             = 3.5

    # List of stress limiter exponents, $n_{\text{lim}}$, for background
    # material and compositional fields, for a total of N+1 values, where N is
    # the number of compositional fields. Units: none.
    set Stress limiter exponents                           = 1.0

    # List of thermal conductivities, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. If only one value is given, then all use the
    # same value. Units: \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivities                             = 3.0

    # List of thermal diffusivities, for background material and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value.  Units: \si{\meter\squared\per\second}.
    set Thermal diffusivities                              = 0.8e-6

    # List of thermal expansivities for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units: \si{\per\kelvin}.
    set Thermal expansivities                              = 0.000035

    # Select whether the material time scale in the viscoelastic constitutive
    # relationship uses the regular numerical time step or a separate fixed
    # elastic time step throughout the model run. The fixed elastic time step
    # is always used during the initial time step. If a fixed elastic time
    # step is used throughout the model run, a stress averaging scheme can be
    # applied to account for differences with the numerical time step. An
    # alternative approach is to limit the maximum time step size so that it
    # is equal to the elastic time step. The default value of this parameter
    # is 'unspecified', which throws an exception during runtime. In order for
    # the model to run the user must select 'true' or 'false'.
    set Use fixed elastic time step                        = unspecified

    # Whether to use a plastic damper when computing the Drucker-Prager
    # plastic viscosity. The damper acts to stabilize the plastic shear band
    # width and remove associated mesh-dependent behavior at sufficient
    # resolutions.
    set Use plastic damper                                 = false

    # Whether to apply a stress averaging scheme to account for differences
    # between the fixed elastic time step and numerical time step.
    set Use stress averaging                               = false

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme                         = harmonic

    # An adjusted viscosity ratio, $E$, for the viscosity approximation, for a
    # total of N+1 values, where N is the number of compositional fields. If
    # only one value is given, then all use the same value. Units: None
    set Viscosity ratios for Frank Kamenetskii             = 15.

    # Select what type of viscosity law to use between diffusion, dislocation,
    # frank kamenetskii, and composite options. Soon there will be an option
    # to select a specific flow law for each assigned composition
    set Viscous flow law                                   = composite

    # Select what type of yield mechanism to use between Drucker Prager and
    # stress limiter options.
    set Yield mechanism                                    = drucker
  end

  subsection Viscoelastic
    # List of densities for background mantle and compositional fields,for a
    # total of N+M+1 values, where N is the number of compositional fields and
    # M is the number of phases. If only one value is given, then all use the
    # same value. Units: \si{\kilogram\per\meter\cubed}.
    set Densities                   = 3300.

    # List of elastic shear moduli, $G$, for background material and
    # compositional fields, for a total of N+1 values, where N is the number
    # of compositional fields. The default value of 75 GPa is representative
    # of mantle rocks. Units: Pa.
    set Elastic shear moduli        = 75.0e9

    # The fixed elastic time step $dte$. Units: years if the 'Use years in
    # output instead of seconds' parameter is set; seconds otherwise.
    set Fixed elastic time step     = 1.e3

    # List of specific heats $C_p$ for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units:
    # \si{\joule\per\kelvin\per\kilogram}.
    set Heat capacities             = 1250.

    # The reference temperature $T_0$. Units: \si{\kelvin}.
    set Reference temperature       = 293.

    # List of thermal conductivities for background mantle and compositional
    # fields, for a total of N+1 values, where N is the number of
    # compositional fields. If only one value is given, then all use the same
    # value. Units: \si{\watt\per\meter\per\kelvin}.
    set Thermal conductivities      = 4.7

    # List of thermal expansivities for background mantle and compositional
    # fields,for a total of N+M+1 values, where N is the number of
    # compositional fields and M is the number of phases. If only one value is
    # given, then all use the same value. Units: \si{\per\kelvin}.
    set Thermal expansivities       = 0.000035

    # Select whether the material time scale in the viscoelastic constitutive
    # relationship uses the regular numerical time step or a separate fixed
    # elastic time step throughout the model run. The fixed elastic time step
    # is always used during the initial time step. If a fixed elastic time
    # step is used throughout the model run, a stress averaging scheme can be
    # applied to account for differences with the numerical time step. An
    # alternative approach is to limit the maximum time step size so that it
    # is equal to the elastic time step. The default value of this parameter
    # is 'unspecified', which throws an exception during runtime. In order for
    # the model to run the user must select 'true' or 'false'.
    set Use fixed elastic time step = unspecified

    # Whether to apply a stress averaging scheme to account for differences
    # between the fixed elastic time step and numerical time step.
    set Use stress averaging        = false

    # List of viscosities for background mantle and compositional fields, for
    # a total of N+1 values, where N is the number of compositional fields. If
    # only one value is given, then all use the same value. Units:
    # \si{\pascal\second}.
    set Viscosities                 = 1.e21

    # When more than one compositional field is present at a point with
    # different viscosities, we need to come up with an average viscosity at
    # that point.  Select a weighted harmonic, arithmetic, geometric, or
    # maximum composition.
    set Viscosity averaging scheme  = harmonic
  end

end


subsection Melt settings
  # Whether to cell-wise average the material properties that are used to
  # compute the melt velocity or not. The melt velocity is computed as the sum
  # of the solid velocity and the phase separation flux $ - K_D / \phi (\nabla
  # p_f - \rho_f \mathbf g)$. If this parameter is set to true, $K_D$ and
  # $\phi$ will be averaged cell-wise in the computation of the phase
  # separation flux. This is useful because in some models the melt velocity
  # can have spikes close to the interface between regions of melt and no
  # melt, as both $K_D$ and $\phi$ go to zero for vanishing melt fraction. As
  # the melt velocity is used for computing the time step size, and in models
  # that use heat transport by melt or shear heating of melt, setting this
  # parameter to true can speed up the model and make it mode stable. In
  # computations where accuracy and convergence behavior of the melt velocity
  # is important (like in benchmark cases with an analytical solution), this
  # parameter should probably be set to 'false'.
  set Average melt velocity                 = true

  # Whether to use a porosity weighted average of the melt and solid velocity
  # to advect heat in the temperature equation or not. If this is set to true,
  # additional terms are assembled on the left-hand side of the temperature
  # advection equation. Only used if Include melt transport is true. If this
  # is set to false, only the solid velocity is used (as in models without
  # melt migration).
  set Heat advection by melt                = false

  # Whether to include the transport of melt into the model or not. If this is
  # set to true, two additional pressures (the fluid pressure and the
  # compaction pressure) will be added to the finite element. Including melt
  # transport in the simulation also requires that there is one compositional
  # field that has the name `porosity'. This field will be used for computing
  # the additional pressures and the melt velocity, and has a different
  # advection equation than other compositional fields, as it is effectively
  # advected with the melt velocity.
  set Include melt transport                = false

  # The factor by how much the Darcy coefficient K\_D in a cell can be smaller
  # than the reference Darcy coefficient for this cell still to be considered
  # a melt cell (for which the melt transport equations are solved). For
  # smaller Darcy coefficients, the Stokes equations (without melt) are solved
  # instead. Only used if ``Include melt transport'' is true.
  set Melt scaling factor threshold         = 1e-7

  # Whether to use a discontinuous element for the compaction pressure or not.
  # From our preliminary tests, continuous elements seem to work better in
  # models where the porosity is > 0 everywhere in the domain, and
  # discontinuous elements work better in models where in parts of the domain
  # the porosity = 0.
  set Use discontinuous compaction pressure = true
end


subsection Mesh deformation
  # A comma separated list of names denoting those boundaries where there the
  # mesh is allowed to move tangential to the boundary. All tangential mesh
  # movements along those boundaries that have tangential material velocity
  # boundary conditions are allowed by default, this parameters allows to
  # generate mesh movements along other boundaries that are open, or have
  # prescribed material velocities or tractions.
  # 
  # The names of the boundaries listed here can either be numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  set Additional tangential mesh velocity boundary indicators = 

  # A comma separated list of names denoting those boundaries where there the
  # mesh is allowed to move according to the specified mesh deformation
  # objects.
  # 
  # The names of the boundaries listed here can either be numbers (in which
  # case they correspond to the numerical boundary indicators assigned by the
  # geometry object), or they can correspond to any of the symbolic names the
  # geometry object may have provided for each part of the boundary. You may
  # want to compare this with the documentation of the geometry model you use
  # in your model.
  # 
  # The format is id1: object1 \& object2, id2: object3 \& object2, where
  # objects are one of `ascii data': Implementation of a model in which the
  # initial mesh deformation (initial topography) is derived from a file
  # containing data in ascii format. The following geometry models are
  # currently supported: box, chunk, spherical. Note the required format of
  # the input data: The first lines may contain any number of comments if they
  # begin with `#', but one of these lines needs to contain the number of grid
  # points in each dimension as for example `# POINTS: 3 3'. The order of the
  # data columns has to be `x', `Topography [m]' in a 2d model and  `x', `y',
  # `Topography [m]' in a 3d model, which means that there has to be a single
  # column containing the topography. Note that the data in the input file
  # needs to be sorted in a specific order: the first coordinate needs to
  # ascend first, followed by the second in order to assign the correct data
  # to the prescribed coordinates. If you use a spherical model, then the
  # assumed grid changes. `x' will be replaced by the azimuth angle in radians
  # and `y' by the polar angle in radians measured positive from the north
  # pole. The grid will be assumed to be a longitude-colatitude grid. Note
  # that the order of spherical coordinates is `phi', `theta' and not `theta',
  # `phi', since this allows for dimension independent expressions.
  # 
  # `boundary function': A plugin, which prescribes the surface mesh to deform
  # according to an analytically prescribed function. Note that the function
  # prescribes a deformation velocity, i.e. the return value of this plugin is
  # later multiplied by the time step length to compute the displacement
  # increment in this time step. Although the function's time variable is
  # interpreted as years when Use years in output instead of seconds is set to
  # true, the boundary deformation velocity should still be given in m/s. The
  # format of the functions follows the syntax understood by the muparser
  # library, see Section~\ref{sec:muparser-format}.
  # 
  # `diffusion': A plugin that computes the deformation of surface vertices
  # according to the solution of the hillslope diffusion problem.
  # Specifically, at the end of each timestep, or after a specific number of
  # timesteps, this plugin solves the following equation: \begin{align*}
  # \frac{\partial h}{\partial t} = \kappa \left( \frac{\partial^{2}
  # h}{\partial x^{2}} + \frac{\partial^{2} h}{\partial y^{2}} \right),
  # \end{align*} where $\kappa$ is the hillslope diffusion coefficient
  # (diffusivity), and $h(x,y)$ the height of a point along the top boundary
  # with respect to the surface of the unperturbed domain.
  # 
  # Using this definition, the plugin then solves for one time step, i.e.,
  # using as initial condition $h(t_{n-1})$ the current surface elevation, and
  # computing $h(t_n)$ from it by solving the equation above over the time
  # interval $t_n-t_{n-1}$. From this, one can then compute a surface velocity
  # $v = \frac{h(t_n)-h(t_{n-1})}{t_n-t_{n-1}}$.
  # 
  # This surface velocity is used to deform the surface and as a boundary
  # condition for solving the Laplace equation to determine the mesh velocity
  # in the domain interior. Diffusion can be applied every timestep, mimicking
  # surface processes of erosion and deposition, or at a user-defined timestep
  # interval to purely smooth the surface topography to avoid too great a
  # distortion of mesh elements when a free surface is also used.
  # 
  # `free surface': A plugin that computes the deformation of surface vertices
  # according to the solution of the flow problem. In particular this means if
  # the surface of the domain is left open to flow, this flow will carry the
  # mesh with it. The implementation was described in \cite{rose_freesurface},
  # with the stabilization of the free surface originally described in
  # \cite{KMM2010}.
  set Mesh deformation boundary indicators                    = 


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory = $ASPECT_SOURCE_DIR/data/geometry-model/initial-topography-model/ascii-data/test/

    # The file name of the model data.
    set Data file name = box_3d_%s.0.txt

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor   = 1.
  end

  subsection Boundary function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Diffusion
    # The hillslope transport coefficient $\kappa$ used to diffuse the free
    # surface, either as a  stabilization step or to mimic erosional and
    # depositional processes. Units: $\si{m^2/s}$.
    set Hillslope transport coefficient = 1e-6

    # The number of time steps between each application of diffusion.
    set Time steps between diffusion    = 1
  end

  subsection Free surface
    # Theta parameter described in \cite{KMM2010}. An unstabilized free
    # surface can overshoot its equilibrium position quite easily and generate
    # unphysical results.  One solution is to use a quasi-implicit correction
    # term to the forces near the free surface.  This parameter describes how
    # much the free surface is stabilized with this term, where zero is no
    # stabilization, and one is fully implicit.
    set Free surface stabilization theta = 0.5

    # After each time step the free surface must be advected in the direction
    # of the velocity field. Mass conservation requires that the mesh velocity
    # is in the normal direction of the surface. However, for steep topography
    # or large curvature, advection in the normal direction can become
    # ill-conditioned, and instabilities in the mesh can form. Projection of
    # the mesh velocity onto the local vertical direction can preserve the
    # mesh quality better, but at the cost of slightly poorer mass
    # conservation of the domain.
    set Surface velocity projection      = normal
  end

end


subsection Mesh refinement
  # Use fraction of the total number of cells instead of fraction of the total
  # error as the limit for refinement and coarsening.
  set Adapt by fraction of cells                          = false

  # A list of times so that if the end time of a time step is beyond this
  # time, an additional round of mesh refinement is triggered. This is mostly
  # useful to make sure we can get through the initial transient phase of a
  # simulation on a relatively coarse mesh, and then refine again when we are
  # in a time range that we are interested in and where we would like to use a
  # finer mesh. Units: Each element of the list has units years if the 'Use
  # years in output instead of seconds' parameter is set; seconds otherwise.
  set Additional refinement times                         = 2.0e8, 2.2e8                # default: 

  # Cells are sorted from largest to smallest by their total error (determined
  # by the Strategy). Then the cells with the smallest error (bottom of this
  # sorted list) that account for the given fraction of the error are
  # coarsened.
  set Coarsening fraction                                 = 0.0                         # default: 0.05

  # The number of adaptive refinement steps performed after initial global
  # refinement but while still within the first time step. These refinement
  # steps (n) are added to the value for initial global refinement (m) so that
  # the final mesh has cells that are at most on refinement level $n+m$.
  set Initial adaptive refinement                         = 0

  # The number of global refinement steps performed on the initial coarse
  # mesh, before the problem is first solved there.
  set Initial global refinement                           = 1                           # default: 2

  # The minimum refinement level each cell should have, and that can not be
  # exceeded by coarsening. Should not be higher than the 'Initial global
  # refinement' parameter.
  set Minimum refinement level                            = 0

  # If multiple refinement criteria are specified in the ``Strategy''
  # parameter, then they need to be combined somehow to form the final
  # refinement indicators. This is done using the method described by the
  # ``Refinement criteria merge operation'' parameter which can either operate
  # on the raw refinement indicators returned by each strategy (i.e.,
  # dimensional quantities) or using normalized values where the indicators of
  # each strategy are first normalized to the interval $[0,1]$ (which also
  # makes them non-dimensional). This parameter determines whether this
  # normalization will happen.
  set Normalize individual refinement criteria            = true

  # If multiple mesh refinement criteria are computed for each cell (by
  # passing a list of more than element to the \texttt{Strategy} parameter in
  # this section of the input file) then one will have to decide which
  # criteria should win when deciding which cells to refine. The operation
  # that determines how to combine these competing criteria is the one that is
  # selected here. The options are:
  # 
  # \begin{itemize}
  # \item \texttt{plus}: Add the various error indicators together and refine
  # those cells on which the sum of indicators is largest.
  # \item \texttt{max}: Take the maximum of the various error indicators and
  # refine those cells on which the maximal indicators is largest.
  # \end{itemize}The refinement indicators computed by each strategy are
  # modified by the ``Normalize individual refinement criteria'' and
  # ``Refinement criteria scale factors'' parameters.
  set Refinement criteria merge operation                 = max

  # A list of scaling factors by which every individual refinement criterion
  # will be multiplied by. If only a single refinement criterion is selected
  # (using the ``Strategy'' parameter, then this parameter has no particular
  # meaning. On the other hand, if multiple criteria are chosen, then these
  # factors are used to weigh the various indicators relative to each other.
  # 
  # If ``Normalize individual refinement criteria'' is set to true, then the
  # criteria will first be normalized to the interval $[0,1]$ and then
  # multiplied by the factors specified here. You will likely want to choose
  # the factors to be not too far from 1 in that case, say between 1 and 10,
  # to avoid essentially disabling those criteria with small weights. On the
  # other hand, if the criteria are not normalized to $[0,1]$ using the
  # parameter mentioned above, then the factors you specify here need to take
  # into account the relative numerical size of refinement indicators (which
  # in that case carry physical units).
  # 
  # You can experimentally play with these scaling factors by choosing to
  # output the refinement indicators into the graphical output of a run.
  # 
  # If the list of indicators given in this parameter is empty, then this
  # indicates that they should all be chosen equal to one. If the list is not
  # empty then it needs to have as many entries as there are indicators chosen
  # in the ``Strategy'' parameter.
  set Refinement criteria scaling factors                 = 

  # Cells are sorted from largest to smallest by their total error (determined
  # by the Strategy). Then the cells with the largest error (top of this
  # sorted list) that account for given fraction of the error are refined.
  set Refinement fraction                                 = 1.0                         # default: 0.3

  # Whether or not the postprocessors should be executed after each of the
  # initial adaptive refinement cycles that are run at the start of the
  # simulation. This is useful for plotting/analyzing how the mesh refinement
  # parameters are working for a particular model.
  set Run postprocessors on initial refinement            = true                        # default: false

  # Whether or not the initial conditions should be set up during the adaptive
  # refinement cycles that are run at the start of the simulation.
  set Skip setup initial conditions on initial refinement = false

  # Whether or not solvers should be executed during the initial adaptive
  # refinement cycles that are run at the start of the simulation.
  set Skip solvers on initial refinement                  = false

  # A comma separated list of mesh refinement criteria that will be run
  # whenever mesh refinement is required. The results of each of these
  # criteria, i.e., the refinement indicators they produce for all the cells
  # of the mesh will then be normalized to a range between zero and one and
  # the results of different criteria will then be merged through the
  # operation selected in this section.
  # 
  # The following criteria are available:
  # 
  # `artificial viscosity': A mesh refinement criterion that computes
  # refinement indicators from the artificial viscosity of the temperature or
  # compositional fields based on user specified weights.
  # 
  # `boundary': A class that implements a mesh refinement criterion which
  # always flags all cells on specified boundaries for refinement. This is
  # useful to provide high accuracy for processes at or close to the edge of
  # the model domain.
  # 
  # To use this refinement criterion, you may want to combine it with other
  # refinement criteria, setting the 'Normalize individual refinement
  # criteria' flag and using the `max' setting for 'Refinement criteria merge
  # operation'.
  # 
  # `compaction length': A mesh refinement criterion for models with melt
  # transport that computes refinement indicators based on the compaction
  # length, defined as $\delta = \sqrt{\frac{(\xi + 4 \eta/3) k}{\eta_f}}$.
  # $\xi$ is the bulk viscosity, $\eta$ is the shear viscosity, $k$ is the
  # permeability and $\eta_f$ is the melt viscosity. If the cell width or
  # height exceeds a multiple (which is specified as an input parameter) of
  # this compaction length, the cell is marked for refinement.
  # 
  # `composition': A mesh refinement criterion that computes refinement
  # indicators from the compositional fields. If there is more than one
  # compositional field, then it simply takes the sum of the indicators
  # computed from each of the compositional field.
  # 
  # The way these indicators are computed is by evaluating the `Kelly error
  # indicator' on each compositional field. This error indicator takes the
  # finite element approximation of the compositional field and uses it to
  # compute an approximation of the second derivatives of the composition for
  # each cell. This approximation is then multiplied by an appropriate power
  # of the cell's diameter to yield an indicator for how large the error is
  # likely going to be on this cell. This construction rests on the
  # observation that for many partial differential equations, the error on
  # each cell is proportional to some power of the cell's diameter times the
  # second derivatives of the solution on that cell.
  # 
  # For complex equations such as those we solve here, this observation may
  # not be strictly true in the mathematical sense, but it often yields meshes
  # that are surprisingly good.
  # 
  # `composition approximate gradient': A mesh refinement criterion that
  # computes refinement indicators from the gradients of compositional fields.
  # If there is more than one compositional field, then it simply takes the
  # sum of the indicators times a user-specified weight for each field.
  # 
  # In contrast to the `composition gradient' refinement criterion, the
  # current criterion does not compute the gradient at quadrature points on
  # each cell, but by a finite difference approximation between the centers of
  # cells. Consequently, it also works if the compositional fields are
  # computed using discontinuous finite elements.
  # 
  # `composition gradient': A mesh refinement criterion that computes
  # refinement indicators from the gradients of compositional fields. If there
  # is more than one compositional field, then it simply takes the sum of the
  # indicators times a user-specified weight for each field.
  # 
  # This refinement criterion computes the gradient of the compositional field
  # at quadrature points on each cell, and then averages them in some way to
  # obtain a refinement indicator for each cell. This will give a reasonable
  # approximation of the true gradient of the compositional field if you are
  # using a continuous finite element.
  # 
  # On the other hand, for discontinuous finite elements (see the `Use
  # discontinuous composition discretization' parameter in the
  # `Discretization' section), the gradient at quadrature points does not
  # include the contribution of jumps in the compositional field between
  # cells, and consequently will not be an accurate approximation of the true
  # gradient. As an extreme example, consider the case of using piecewise
  # constant finite elements for compositional fields; in that case, the
  # gradient of the solution at quadrature points inside each cell will always
  # be exactly zero, even if the finite element solution is different from
  # each cell to the next. Consequently, the current refinement criterion will
  # likely not be useful in this situation. That said, the `composition
  # approximate gradient' refinement criterion exists for exactly this
  # purpose.
  # 
  # `composition threshold': A mesh refinement criterion that computes
  # refinement indicators from the compositional fields. If any field exceeds
  # the threshold given in the input file, the cell is marked for refinement.
  # 
  # `density': A mesh refinement criterion that computes refinement indicators
  # from a field that describes the spatial variability of the density,
  # $\rho$. Because this quantity may not be a continuous function ($\rho$ and
  # $C_p$ may be discontinuous functions along discontinuities in the medium,
  # for example due to phase changes), we approximate the gradient of this
  # quantity to refine the mesh. The error indicator defined here takes the
  # magnitude of the approximate gradient and scales it by $h_K^{1+d/2}$ where
  # $h_K$ is the diameter of each cell and $d$ is the dimension. This scaling
  # ensures that the error indicators converge to zero as $h_K\rightarrow 0$
  # even if the energy density is discontinuous, since the gradient of a
  # discontinuous function grows like $1/h_K$.
  # 
  # `maximum refinement function': A mesh refinement criterion that ensures a
  # maximum refinement level described by an explicit formula with the depth
  # or position as argument. Which coordinate representation is used is
  # determined by an input parameter. Whatever the coordinate system chosen,
  # the function you provide in the input file will by default depend on
  # variables `x', `y' and `z' (if in 3d). However, the meaning of these
  # symbols depends on the coordinate system. In the Cartesian coordinate
  # system, they simply refer to their natural meaning. If you have selected
  # `depth' for the coordinate system, then `x' refers to the depth variable
  # and `y' and `z' will simply always be zero. If you have selected a
  # spherical coordinate system, then `x' will refer to the radial distance of
  # the point to the origin, `y' to the azimuth angle and `z' to the polar
  # angle measured positive from the north pole. Note that the order of
  # spherical coordinates is r,phi,theta and not r,theta,phi, since this
  # allows for dimension independent expressions. Each coordinate system also
  # includes a final `t' variable which represents the model time, evaluated
  # in years if the 'Use years in output instead of seconds' parameter is set,
  # otherwise evaluated in seconds. After evaluating the function, its values
  # are rounded to the nearest integer.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `minimum refinement function': A mesh refinement criterion that ensures a
  # minimum refinement level described by an explicit formula with the depth
  # or position as argument. Which coordinate representation is used is
  # determined by an input parameter. Whatever the coordinate system chosen,
  # the function you provide in the input file will by default depend on
  # variables `x', `y' and `z' (if in 3d). However, the meaning of these
  # symbols depends on the coordinate system. In the Cartesian coordinate
  # system, they simply refer to their natural meaning. If you have selected
  # `depth' for the coordinate system, then `x' refers to the depth variable
  # and `y' and `z' will simply always be zero. If you have selected a
  # spherical coordinate system, then `x' will refer to the radial distance of
  # the point to the origin, `y' to the azimuth angle and `z' to the polar
  # angle measured positive from the north pole. Note that the order of
  # spherical coordinates is r,phi,theta and not r,theta,phi, since this
  # allows for dimension independent expressions. Each coordinate system also
  # includes a final `t' variable which represents the model time, evaluated
  # in years if the 'Use years in output instead of seconds' parameter is set,
  # otherwise evaluated in seconds. After evaluating the function, its values
  # are rounded to the nearest integer.
  # 
  # The format of these functions follows the syntax understood by the
  # muparser library, see Section~\ref{sec:muparser-format}.
  # 
  # `nonadiabatic temperature': A mesh refinement criterion that computes
  # refinement indicators from the excess temperature(difference between
  # temperature and adiabatic temperature.
  # 
  # `particle density': A mesh refinement criterion that computes refinement
  # indicators based on the density of particles. In practice this plugin
  # equilibrates the number of particles per cell, leading to fine cells in
  # high particle density regions and coarse cells in low particle density
  # regions. This plugin is mostly useful for models with inhomogeneous
  # particle density, e.g. when tracking an initial interface with a high
  # particle density, or when the spatial particle density denotes the region
  # of interest. Additionally, this plugin tends to balance the computational
  # load between processes in parallel computations, because the particle and
  # mesh density is more aligned.
  # 
  # `slope': A class that implements a mesh refinement criterion intended for
  # use with deforming mesh boundaries, like the free surface. It calculates a
  # local slope based on the angle between the surface normal and the local
  # gravity vector. Cells with larger angles are marked for refinement.
  # 
  # To use this refinement criterion, you may want to combine it with other
  # refinement criteria, setting the 'Normalize individual refinement
  # criteria' flag and using the `max' setting for 'Refinement criteria merge
  # operation'.
  # 
  # `strain rate': A mesh refinement criterion that computes the refinement
  # indicators equal to the strain rate norm computed at the center of the
  # elements.
  # 
  # `temperature': A mesh refinement criterion that computes refinement
  # indicators from the temperature field.
  # 
  # The way these indicators are computed is by evaluating the `Kelly error
  # indicator' on the temperature field. This error indicator takes the finite
  # element approximation of the temperature field and uses it to compute an
  # approximation of the second derivatives of the temperature for each cell.
  # This approximation is then multiplied by an appropriate power of the
  # cell's diameter to yield an indicator for how large the error is likely
  # going to be on this cell. This construction rests on the observation that
  # for many partial differential equations, the error on each cell is
  # proportional to some power of the cell's diameter times the second
  # derivatives of the solution on that cell.
  # 
  # For complex equations such as those we solve here, this observation may
  # not be strictly true in the mathematical sense, but it often yields meshes
  # that are surprisingly good.
  # 
  # `thermal energy density': A mesh refinement criterion that computes
  # refinement indicators from a field that describes the spatial variability
  # of the thermal energy density, $\rho C_p T$. Because this quantity may not
  # be a continuous function ($\rho$ and $C_p$ may be discontinuous functions
  # along discontinuities in the medium, for example due to phase changes), we
  # approximate the gradient of this quantity to refine the mesh. The error
  # indicator defined here takes the magnitude of the approximate gradient and
  # scales it by $h_K^{1.5}$ where $h_K$ is the diameter of each cell. This
  # scaling ensures that the error indicators converge to zero as
  # $h_K\rightarrow 0$ even if the energy density is discontinuous, since the
  # gradient of a discontinuous function grows like $1/h_K$.
  # 
  # `topography': A class that implements a mesh refinement criterion, which
  # always flags all cells in the uppermost layer for refinement. This is
  # useful to provide high accuracy for processes at or close to the surface.
  # 
  # To use this refinement criterion, you may want to combine it with other
  # refinement criteria, setting the 'Normalize individual refinement
  # criteria' flag and using the `max' setting for 'Refinement criteria merge
  # operation'.
  # 
  # `velocity': A mesh refinement criterion that computes refinement
  # indicators from the velocity field.
  # 
  # The way these indicators are computed is by evaluating the `Kelly error
  # indicator' on the velocity field. This error indicator takes the finite
  # element approximation of the velocity field and uses it to compute an
  # approximation of the second derivatives of the velocity for each cell.
  # This approximation is then multiplied by an appropriate power of the
  # cell's diameter to yield an indicator for how large the error is likely
  # going to be on this cell. This construction rests on the observation that
  # for many partial differential equations, the error on each cell is
  # proportional to some power of the cell's diameter times the second
  # derivatives of the solution on that cell.
  # 
  # For complex equations such as those we solve here, this observation may
  # not be strictly true in the mathematical sense, but it often yields meshes
  # that are surprisingly good.
  # 
  # `viscosity': A mesh refinement criterion that computes refinement
  # indicators from a field that describes the spatial variability of the
  # logarithm of the viscosity, $\log\eta$. (We choose the logarithm of the
  # viscosity because it can vary by orders of magnitude.)Because this
  # quantity may not be a continuous function ($\eta$ may be a discontinuous
  # function along discontinuities in the medium, for example due to phase
  # changes), we approximate the gradient of this quantity to refine the mesh.
  # The error indicator defined here takes the magnitude of the approximate
  # gradient and scales it by $h_K^{1+d/2}$ where $h_K$ is the diameter of
  # each cell and $d$ is the dimension. This scaling ensures that the error
  # indicators converge to zero as $h_K\rightarrow 0$ even if the energy
  # density is discontinuous, since the gradient of a discontinuous function
  # grows like $1/h_K$.
  # 
  # `volume of fluid interface': A class that implements a mesh refinement
  # criterion, which ensures a minimum level of refinement near the volume of
  # fluid interface boundary.
  set Strategy                                            = minimum refinement function # default: thermal energy density

  # The number of time steps after which the mesh is to be adapted again based
  # on computed error indicators. If 0 then the mesh will never be changed.
  set Time steps between mesh refinement                  = 0                           # default: 10


  subsection Artificial viscosity
    # A list of scaling factors by which every individual compositional field
    # will be multiplied. These factors are used to weigh the various
    # indicators relative to each other and to the temperature.
    # 
    # If the list of scaling factors given in this parameter is empty, then
    # this indicates that they should all be chosen equal to 0. If the list is
    # not empty then it needs to have as many entries as there are
    # compositional fields.
    set Compositional field scaling factors = 

    # A scaling factor for the artificial viscosity  of the temperature
    # equation. Use 0.0 to disable.
    set Temperature scaling factor          = 0.0
  end

  subsection Boundary
    # A comma separated list of names denoting those boundaries where there
    # should be mesh refinement.
    # 
    # The names of the boundaries listed here can either be numbers (in which
    # case they correspond to the numerical boundary indicators assigned by
    # the geometry object), or they can correspond to any of the symbolic
    # names the geometry object may have provided for each part of the
    # boundary. You may want to compare this with the documentation of the
    # geometry model you use in your model.
    set Boundary refinement indicators = 
  end

  subsection Compaction length
    # The desired ratio between compaction length and size of the mesh cells,
    # or, in other words, how many cells the mesh should (at least) have per
    # compaction length. Every cell where this ratio is smaller than the value
    # specified by this parameter (in places with fewer mesh cells per
    # compaction length) is marked for refinement.
    set Mesh cells per compaction length = 1.0
  end

  subsection Composition
    # A list of scaling factors by which every individual compositional field
    # will be multiplied. If only a single compositional field exists, then
    # this parameter has no particular meaning. On the other hand, if multiple
    # criteria are chosen, then these factors are used to weigh the various
    # indicators relative to each other.
    # 
    # If the list of scaling factors given in this parameter is empty, then
    # this indicates that they should all be chosen equal to one. If the list
    # is not empty then it needs to have as many entries as there are
    # compositional fields.
    set Compositional field scaling factors = 
  end

  subsection Composition approximate gradient
    # A list of scaling factors by which every individual compositional field
    # gradient will be multiplied. If only a single compositional field
    # exists, then this parameter has no particular meaning. On the other
    # hand, if multiple criteria are chosen, then these factors are used to
    # weigh the various indicators relative to each other.
    # 
    # If the list of scaling factors given in this parameter is empty, then
    # this indicates that they should all be chosen equal to one. If the list
    # is not empty then it needs to have as many entries as there are
    # compositional fields.
    set Compositional field scaling factors = 
  end

  subsection Composition gradient
    # A list of scaling factors by which every individual compositional field
    # gradient will be multiplied. If only a single compositional field
    # exists, then this parameter has no particular meaning. On the other
    # hand, if multiple criteria are chosen, then these factors are used to
    # weigh the various indicators relative to each other.
    # 
    # If the list of scaling factors given in this parameter is empty, then
    # this indicates that they should all be chosen equal to one. If the list
    # is not empty then it needs to have as many entries as there are
    # compositional fields.
    set Compositional field scaling factors = 
  end

  subsection Composition threshold
    # A list of thresholds that every individual compositional field will be
    # evaluated against.
    set Compositional field thresholds = 
  end

  subsection Maximum refinement function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `depth', `cartesian' and
    # `spherical'. `depth' will create a function, in which only the first
    # variable is non-zero, which is interpreted to be the depth of the point.
    # `spherical' coordinates are interpreted as r,phi or r,phi,theta in 2D/3D
    # respectively with theta being the polar angle.
    set Coordinate system   = depth

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Minimum refinement function
    # A selection that determines the assumed coordinate system for the
    # function variables. Allowed values are `depth', `cartesian' and
    # `spherical'. `depth' will create a function, in which only the first
    # variable is non-zero, which is interpreted to be the depth of the point.
    # `spherical' coordinates are interpreted as r,phi or r,phi,theta in 2D/3D
    # respectively with theta being the polar angle.
    set Coordinate system   = depth

    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 7.0   # default: 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Volume of fluid interface
    # If true, then explicitly coarsen any cells not neighboring the
    # VolumeOfFluid interface.
    set Strict coarsening = false
  end

end


subsection Nullspace removal
  # Choose none, one or several from
  # 
  # \begin{itemize} \item net rotation \item angular momentum \item net
  # translation \item net surface rotation\item linear momentum \item net x
  # translation \item net y translation \item net z translation \item linear x
  # momentum \item linear y momentum \item linear z momentum \end{itemize}
  # 
  # These are a selection of operations to remove certain parts of the
  # nullspace from the velocity after solving. For some geometries and certain
  # boundary conditions the velocity field is not uniquely determined but
  # contains free translations and/or rotations. Depending on what you specify
  # here, these non-determined modes will be removed from the velocity field
  # at the end of the Stokes solve step.
  # 
  # 
  # The ``angular momentum'' option removes a rotation such that the net
  # angular momentum is zero. The ``linear * momentum'' options remove
  # translations such that the net momentum in the relevant direction is zero.
  # The ``net rotation'' option removes the net rotation of the whole domain,
  # the ``net surface rotation'' option removes the net rotation of the top
  # surface, and the ``net * translation'' options remove the net translations
  # in the relevant directions.  For most problems there should not be a
  # significant difference between the momentum and rotation/translation
  # versions of nullspace removal, although the momentum versions are more
  # physically motivated. They are equivalent for constant density
  # simulations, and approximately equivalent when the density variations are
  # small.
  # 
  # Note that while more than one operation can be selected it only makes
  # sense to pick one rotational and one translational operation.
  set Remove nullspace = 
end


subsection Postprocess
  # A comma separated list of postprocessor objects that should be run at the
  # end of each time step. Some of these postprocessors will declare their own
  # parameters which may, for example, include that they will actually do
  # something only every so many time steps or years. Alternatively, the text
  # `all' indicates that all available postprocessors should be run after each
  # time step.
  # 
  # The following postprocessors are available:
  # 
  # `Stokes residual': A postprocessor that outputs the Stokes residuals
  # during the iterative solver algorithm into a file stokes_residuals.txt in
  # the output directory.
  # 
  # `basic statistics': A postprocessor that outputs some simplified
  # statistics like the Rayleigh number and other quantities that only make
  # sense in certain model setups. The output is written after completing
  # initial adaptive refinement steps. The postprocessor assumes a point at
  # the surface at the adiabatic surface temperature and pressure is a
  # reasonable reference condition for computing these properties.
  # Furthermore, the Rayleigh number is computed using the model depth (i.e.
  # not the radius of the Earth), as we need a definition that is geometry
  # independent. Take care when comparing these values to published studies
  # and make sure they use the same definitions.
  # 
  # `boundary densities': A postprocessor that computes the laterally averaged
  # density at the top and bottom of the domain.
  # 
  # `boundary pressures': A postprocessor that computes the laterally averaged
  # pressure at the top and bottom of the domain.
  # 
  # `boundary velocity residual statistics': A postprocessor that computes
  # some statistics about the velocity residual along the top boundary. The
  # velocity residual is the difference between the model solution velocities
  # and the input velocities (GPlates model or ascii data). Currently, the
  # velocity residual statistics, i.e., min, max and the rms magnitude, is
  # computed at the top suface.
  # 
  # `command': A postprocessor that executes a command line process.
  # 
  # `composition statistics': A postprocessor that computes some statistics
  # about the compositional fields, if present in this simulation. In
  # particular, it computes maximal and minimal values of each field, as well
  # as the total mass contained in this field as defined by the integral
  # $m_i(t) = \int_\Omega c_i(\mathbf x,t) \; \text{d}x$.
  # 
  # `core statistics': A postprocessor that computes some statistics about the
  # core evolution. (Working only with dynamic core boundary temperature
  # plugin)
  # 
  # `depth average': A postprocessor that computes depth averaged quantities
  # and writes them into a file <depth_average.ext> in the output directory,
  # where the extension of the file is determined by the output format you
  # select. In addition to the output format, a number of other parameters
  # also influence this postprocessor, and they can be set in the section
  # \texttt{Postprocess/Depth average} in the input file.
  # 
  # In the output files, the $x$-value of each data point corresponds to the
  # depth, whereas the $y$-value corresponds to the simulation time. The time
  # is provided in seconds or, if the global ``Use years in output instead of
  # seconds'' parameter is set, in years.
  # 
  # `dynamic topography': A postprocessor that computes a measure of dynamic
  # topography based on the stress at the surface and bottom. The data is
  # written into text files named `dynamic\_topography.NNNNN' in the output
  # directory, where NNNNN is the number of the time step.
  # 
  # The exact approach works as follows: At the centers of all cells that sit
  # along the top surface, we evaluate the stress and evaluate the component
  # of it in the direction in which gravity acts. In other words, we compute
  # $\sigma_{rr}={\hat g}^T(2 \eta \varepsilon(\mathbf u)- \frac 13
  # (\textrm{div}\;\mathbf u)I)\hat g - p_d$ where $\hat g = \mathbf
  # g/\|\mathbf g\|$ is the direction of the gravity vector $\mathbf g$ and
  # $p_d=p-p_a$ is the dynamic pressure computed by subtracting the adiabatic
  # pressure $p_a$ from the total pressure $p$ computed as part of the Stokes
  # solve. From this, the dynamic topography is computed using the formula
  # $h=\frac{\sigma_{rr}}{(\mathbf g \cdot \mathbf n)  \rho}$ where $\rho$ is
  # the density at the cell center. For the bottom surface we chose the
  # convection that positive values are up (out) and negative values are in
  # (down), analogous to the deformation of the upper surface. Note that this
  # implementation takes the direction of gravity into account, which means
  # that reversing the flow in backward advection calculations will not
  # reverse the instantaneous topography because the reverse flow will be
  # divided by the reverse surface gravity.
  # The file format then consists of lines with Euclidean coordinates followed
  # by the corresponding topography value.
  # 
  # (As a side note, the postprocessor chooses the cell center instead of the
  # center of the cell face at the surface, where we really are interested in
  # the quantity, since this often gives better accuracy. The results should
  # in essence be the same, though.)
  # 
  # `entropy viscosity statistics': A postprocessor that computes the maximum
  # and volume averagedentropy viscosity stabilization for the temperature
  # field.
  # 
  # `geoid': A postprocessor that computes a representation of the geoid based
  # on the density structure in the mantle, as well as the dynamic topography
  # at the surface and core mantle boundary (CMB). The geoid is computed from
  # a spherical harmonic expansion, so the geometry of the domain must be a 3D
  # spherical shell.
  # 
  # `global statistics': A postprocessor that outputs all the global
  # statistics information, e.g. the time of the simulation, the timestep
  # number, number of degrees of freedom and solver iterations for each
  # timestep. The postprocessor can output different formats, the first
  # printing one line in the statistics file per nonlinear solver iteration
  # (if a nonlinear solver scheme is selected). The second prints one line per
  # timestep, summing the information about all nonlinear iterations in this
  # line. Note that this postprocessor is always active independent on whether
  # or not it is selected in the parameter file.
  # 
  # `gravity calculation': A postprocessor that computes gravity, gravity
  # anomalies, gravity potential and gravity gradients for a set of points
  # (e.g. satellites) in or above the model surface for either a user-defined
  # range of latitudes, longitudes and radius or a list of point
  # coordinates.Spherical coordinates in the output file are radius,
  # colatitude and colongitude. Gravity is here based on the density
  # distribution from the material model (and non adiabatic). This means that
  # the density may come directly from an ascii file. This postprocessor also
  # computes theoretical gravity and its derivatives, which corresponds to the
  # analytical solution of gravity in the same geometry but filled with a
  # reference density. The reference density is also used to determine density
  # anomalies for computing gravity anomalies. Thus one must carefully
  # evaluate the meaning of the gravity anomaly output, because the solution
  # may not reflect the actual gravity anomaly (due to differences in the
  # assumed reference density). On way to guarantee correct gravity anomalies
  # is to subtract gravity of a certain point from the average gravity on the
  # map. Another way is to directly use density anomalies for this
  # postprocessor.The average- minimum- and maximum gravity acceleration and
  # potential are written into the statistics file.
  # 
  # `heat flux densities': A postprocessor that computes some statistics about
  # the heat flux density for each boundary id. The heat flux density across
  # each boundary is computed in outward direction, i.e., from the domain to
  # the outside. The heat flux is computed as sum of advective heat flux and
  # conductive heat flux through Neumann boundaries, both computed as integral
  # over the boundary area, and conductive heat flux through Dirichlet
  # boundaries, which is computed using the consistent boundary flux method as
  # described in ``Gresho, Lee, Sani, Maslanik, Eaton (1987). The consistent
  # Galerkin FEM for computing derived boundary quantities in thermal and or
  # fluids problems. International Journal for Numerical Methods in Fluids,
  # 7(4), 371-394.''
  # 
  # Note that the ``heat flux statistics'' postprocessor computes the same
  # quantity as the one here, but not divided by the area of the surface. In
  # other words, it computes the \textit{total} heat flux through each
  # boundary.
  # 
  # `heat flux map': A postprocessor that computes the heat flux density
  # across each boundary in outward direction, i.e., from the domain to the
  # outside. The heat flux is computed as sum of advective heat flux and
  # conductive heat flux through Neumann boundaries, both computed as integral
  # over the boundary area, and conductive heat flux through Dirichlet
  # boundaries, which is computed using the consistent boundary flux method as
  # described in ``Gresho, Lee, Sani, Maslanik, Eaton (1987). The consistent
  # Galerkin FEM for computing derived boundary quantities in thermal and or
  # fluids problems. International Journal for Numerical Methods in Fluids,
  # 7(4), 371-394.''
  # 
  # `heat flux statistics': A postprocessor that computes some statistics
  # about the heat flux density across each boundary in outward direction,
  # i.e., from the domain to the outside. The heat flux is computed as sum of
  # advective heat flux and conductive heat flux through Neumann boundaries,
  # both computed as integral over the boundary area, and conductive heat flux
  # through Dirichlet boundaries, which is computed using the consistent
  # boundary flux method as described in ``Gresho, Lee, Sani, Maslanik, Eaton
  # (1987). The consistent Galerkin FEM for computing derived boundary
  # quantities in thermal and or fluids problems. International Journal for
  # Numerical Methods in Fluids, 7(4), 371-394.''The point-wise heat flux can
  # be obtained from the heat flux map postprocessor, which outputs the heat
  # flux to a file, or the heat flux map visualization postprocessor, which
  # outputs the heat flux for visualization.
  # 
  # As stated, this postprocessor computes the \textit{outbound} heat flux. If
  # you are interested in the opposite direction, for example from the core
  # into the mantle when the domain describes the mantle, then you need to
  # multiply the result by -1.
  # 
  # \note{In geodynamics, the term ``heat flux'' is often understood to be the
  # quantity $- k \nabla T$, which is really a heat flux \textit{density},
  # i.e., a vector-valued field. In contrast to this, the current
  # postprocessor only computes the integrated flux over each part of the
  # boundary. Consequently, the units of the quantity computed here are
  # $W=\frac{J}{s}$.}
  # 
  # The ``heat flux densities'' postprocessor computes the same quantity as
  # the one here, but divided by the area of the surface.
  # 
  # `heating statistics': A postprocessor that computes some statistics about
  # heating, averaged by volume.
  # 
  # `load balance statistics': A postprocessor that computes statistics about
  # the distribution of cells, and if present particles across subdomains. In
  # particular, it computes maximal, average and minimal number of cells
  # across all ranks. If there are particles it also computes the maximal,
  # average, and minimum number of particles across all ranks, and maximal,
  # average, and minimal ratio between local number of particles and local
  # number of cells across all processes. All of these numbers can be useful
  # to assess the load balance between different MPI ranks, as the difference
  # between the mimimal and maximal load should be as small as possible.
  # 
  # `mass flux statistics': A postprocessor that computes some statistics
  # about the mass flux across boundaries. For each boundary indicator (see
  # your geometry description for which boundary indicators are used), the
  # mass flux is computed in outward direction, i.e., from the domain to the
  # outside, using the formula $\int_{\Gamma_i} \rho \mathbf v \cdot \mathbf
  # n$ where $\Gamma_i$ is the part of the boundary with indicator $i$, $\rho$
  # is the density as reported by the material model, $\mathbf v$ is the
  # velocity, and $\mathbf n$ is the outward normal.
  # 
  # As stated, this postprocessor computes the \textit{outbound} mass flux. If
  # you are interested in the opposite direction, for example from the core
  # into the mantle when the domain describes the mantle, then you need to
  # multiply the result by -1.
  # 
  # \note{In geodynamics, the term ``mass flux'' is often understood to be the
  # quantity $\rho \mathbf v$, which is really a mass flux \textit{density},
  # i.e., a vector-valued field. In contrast to this, the current
  # postprocessor only computes the integrated flux over each part of the
  # boundary. Consequently, the units of the quantity computed here are
  # $\frac{kg}{s}$.}
  # 
  # `material statistics': A postprocessor that computes some statistics about
  # the material properties. In particular, it computes the volume-averages of
  # the density and viscosity, and the total mass in the model. Specifically,
  # it implements the following formulas in each time step: $\left<\rho\right>
  # = \frac{1}{|\Omega|} \int_\Omega \rho(\mathbf x) \, \text{d}x$,
  # $\left<\eta\right> = \frac{1}{|\Omega|} \int_\Omega \eta(\mathbf x) \,
  # \text{d}x$, $M = \int_\Omega \rho(\mathbf x) \, \text{d}x$, where
  # $|\Omega|$ is the volume of the domain.
  # 
  # `matrix statistics': A postprocessor that computes some statistics about
  # the matrices. In particular, it outputs total memory consumption, total
  # non-zero elements, and non-zero elements per block, for system matrix and
  # system preconditioner matrix.
  # 
  # `melt statistics': A postprocessor that computes some statistics about the
  # melt (volume) fraction. If the material model does not implement a melt
  # fraction function, the output is set to zero.
  # 
  # `memory statistics': A postprocessor that computes some statistics about
  # the memory consumption. In particular, it computes the memory usage of the
  # system matrix, triangulation, p4est, DoFHandler, current constraints,
  # solution vector, and peak virtual memory usage, all in MB. It also outputs
  # the memory usage of the system matrix to the screen.
  # 
  # `particle count statistics': A postprocessor that computes some statistics
  # about the particle distribution, if present in this simulation. In
  # particular, it computes minimal, average and maximal values of particles
  # per cell in the global domain.
  # 
  # `particles': A Postprocessor that creates particles that follow the
  # velocity field of the simulation. The particles can be generated and
  # propagated in various ways and they can carry a number of constant or
  # time-varying properties. The postprocessor can write output positions and
  # properties of all particles at chosen intervals, although this is not
  # mandatory. It also allows other parts of the code to query the particles
  # for information.
  # 
  # `point values': A postprocessor that evaluates the solution (i.e.,
  # velocity, pressure, temperature, and compositional fields along with other
  # fields that are treated as primary variables) at the end of every time
  # step or after a user-specified time interval at a given set of points and
  # then writes this data into the file <point\_values.txt> in the output
  # directory. The points at which the solution should be evaluated are
  # specified in the section \texttt{Postprocess/Point values} in the input
  # file.
  # 
  # In the output file, data is organized as (i) time, (ii) the 2 or 3
  # coordinates of the evaluation points, and (iii) followed by the values of
  # the solution vector at this point. The time is provided in seconds or, if
  # the global ``Use years in output instead of seconds'' parameter is set, in
  # years. In the latter case, the velocity is also converted to meters/year,
  # instead of meters/second.
  # 
  # \note{Evaluating the solution of a finite element field at arbitrarily
  # chosen points is an expensive process. Using this postprocessor will only
  # be efficient if the number of evaluation points or output times is
  # relatively small. If you need a very large number of evaluation points,
  # you should consider extracting this information from the visualization
  # program you use to display the output of the `visualization'
  # postprocessor.}
  # 
  # `pressure statistics': A postprocessor that computes some statistics about
  # the pressure field.
  # 
  # `rotation statistics': A postprocessor that computes some statistics about
  # the rotational velocity of the model (i.e. integrated net rotation and
  # angular momentum). In 2D we assume the model to be a cross-section through
  # an infinite domain in z direction, with a zero z-velocity. Thus, the
  # z-axis is the only possible rotation axis and both moment of inertia and
  # angular momentum are scalar instead of tensor quantities.
  # 
  # `spherical velocity statistics': A postprocessor that computes radial,
  # tangential and total RMS velocity.
  # 
  # `temperature statistics': A postprocessor that computes some statistics
  # about the temperature field.
  # 
  # `topography': A postprocessor intended for use with a deforming top
  # surface.  After every step it loops over all the vertices on the top
  # surface and determines the maximum and minimum topography relative to a
  # reference datum (initial box height for a box geometry model or initial
  # radius for a sphere/spherical shell geometry model). If 'Topography.Output
  # to file' is set to true, also outputs topography into text files named
  # `topography.NNNNN' in the output directory, where NNNNN is the number of
  # the time step.
  # The file format then consists of lines with Euclidean coordinates followed
  # by the corresponding topography value.Topography is printed/written in
  # meters.
  # 
  # `velocity boundary statistics': A postprocessor that computes some
  # statistics about the velocity along the boundaries. For each boundary
  # indicator (see your geometry description for which boundary indicators are
  # used), the min and max velocity magnitude is computed.
  # 
  # `velocity statistics': A postprocessor that computes some statistics about
  # the velocity field.
  # 
  # `visualization': A postprocessor that takes the solution and writes it
  # into files that can be read by a graphical visualization program.
  # Additional run time parameters are read from the parameter subsection
  # 'Visualization'.
  # 
  # `volume of fluid statistics': A postprocessor that computes some
  # statistics about the volume-of-fluid fields.
  set List of postprocessors                     = visualization, temperature statistics, velocity statistics # default: 

  # Whether or not the postprocessors should be executed after each of the
  # nonlinear iterations done within one time step. As this is mainly an
  # option for the purposes of debugging, it is not supported when the 'Time
  # between graphical output' is larger than zero, or when the postprocessor
  # is not intended to be run more than once per timestep.
  set Run postprocessors on nonlinear iterations = false


  subsection Boundary velocity residual statistics
    # The name of a directory that contains the GPlates model or the ascii
    # data. This path may either be absolute (if starting with a `/') or
    # relative to the current directory. The path may also include the special
    # text `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
    # the ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory             = $ASPECT_SOURCE_DIR/data/boundary-velocity/gplates/

    # The file name of the input velocity as a GPlates model or an ascii data.
    # For the GPlates model, provide file in the same format as described in
    # the 'gplates' boundary velocity plugin. For the ascii data, provide file
    # in the same format as described in  'ascii data' initial composition
    # plugin.
    set Data file name             = current_day.gpml

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor               = 1.

    # Use ascii data files (e.g., GPS) for computing residual velocities
    # instead of GPlates data.
    set Use ascii data             = false

    # Specify velocity as r, phi, and theta components instead of x, y, and z.
    # Positive velocities point up, east, and north (in 3D) or out and
    # clockwise (in 2D). This setting only makes sense for spherical
    # geometries.GPlates data is always interpreted to be in east and north
    # directions and is not affected by this parameter.
    set Use spherical unit vectors = false
  end

  subsection Command
    # Command to execute.
    set Command              = 

    # Whether to run command from all processes (true), or only on process 0
    # (false).
    set Run on all processes = false

    # Select whether \aspect{} should terminate if the command returns a
    # non-zero exit status.
    set Terminate on failure = false
  end

  subsection Depth average
    # The depth boundaries of zones within which we are to compute averages.
    # By default this list is empty and we subdivide the entire domain into
    # equidistant depth zones and compute averages within each of these zones.
    # If this list is not empty it has to contain one more entry than the
    # 'Number of zones' parameter, representing the upper and lower depth
    # boundary of each zone. It is not necessary to cover the whole
    # depth-range (i.e. you can select to only average in a single layer by
    # choosing 2 arbitrary depths as the boundaries of that layer).
    set Depth boundaries of zones     = 

    # A comma separated list which specifies which quantities to average in
    # each depth slice. It defaults to averaging all available quantities, but
    # this can be an expensive operation, so you may want to select only a
    # few.
    # 
    # List of options:
    # all|temperature|composition|adiabatic temperature|adiabatic
    # pressure|adiabatic density|adiabatic density derivative|velocity
    # magnitude|sinking velocity|Vs|Vp|viscosity|vertical heat flux|vertical
    # mass flux|composition mass
    set List of output variables      = all

    # The number of zones in depth direction within which we are to compute
    # averages. By default, we subdivide the entire domain into 10 depth zones
    # and compute temperature and other averages within each of these zones.
    # However, if you have a very coarse mesh, it may not make much sense to
    # subdivide the domain into so many zones and you may wish to choose less
    # than this default. It may also make computations slightly faster. On the
    # other hand, if you have an extremely highly resolved mesh, choosing more
    # zones might also make sense.
    set Number of zones               = 10

    # A list of formats in which the output shall be produced. The format in
    # which the output is generated also determines the extension of the file
    # into which data is written. The list of possible output formats that can
    # be given here is documented in the appendix of the manual where the
    # current parameter is described. By default the output is written as
    # gnuplot file (for plotting), and as a simple text file.
    set Output format                 = gnuplot, txt

    # The time interval between each generation of graphical output files. A
    # value of zero indicates that output should be generated in each time
    # step. Units: years if the 'Use years in output instead of seconds'
    # parameter is set; seconds otherwise.
    set Time between graphical output = 1e8
  end

  subsection Dynamic core statistics
    # Output the excess entropy only instead the each entropy terms.
    set Excess entropy only = false
  end

  subsection Dynamic topography
    # Dynamic topography is calculated as the excess or lack of mass that is
    # supported by mantle flow. This value depends on the density of material
    # that is moved up or down, i.e. crustal rock, and the density of the
    # material that is displaced (generally water or air). While the density
    # of crustal rock is part of the material model, this parameter `Density
    # above' allows the user to specify the density value of material that is
    # displaced above the solid surface. By default this material is assumed
    # to be air, with a density of 0. Units: \si{\kilogram\per\meter\cubed}.
    set Density above  = 0.

    # Dynamic topography is calculated as the excess or lack of mass that is
    # supported by mantle flow. This value depends on the density of material
    # that is moved up or down, i.e. mantle above CMB, and the density of the
    # material that is displaced (generally outer core material). While the
    # density of mantle rock is part of the material model, this parameter
    # `Density below' allows the user to specify the density value of material
    # that is displaced below the solid surface. By default this material is
    # assumed to be outer core material with a density of 9900. Units:
    # \si{\kilogram\per\meter\cubed}.
    set Density below  = 9900.

    # Whether to output a file containing the bottom (i.e., CMB) dynamic
    # topography.
    set Output bottom  = true

    # Whether to output a file containing the surface dynamic topography.
    set Output surface = true
  end

  subsection Geoid
    # Option to also output the free-air gravity anomaly up to the maximum
    # degree. The unit of the output is in SI, hence $m/s^2$ ($1mgal = 10^-5
    # m/s^2$). The default is false.
    set Also output the gravity anomaly                                                            = false

    # Option to also output the spherical harmonic coefficients of the CMB
    # dynamic topography contribution to the maximum degree. The default is
    # false.
    set Also output the spherical harmonic coefficients of CMB dynamic topography contribution     = false

    # Option to also output the spherical harmonic coefficients of the density
    # anomaly contribution to the maximum degree. The default is false.
    set Also output the spherical harmonic coefficients of density anomaly contribution            = false

    # Option to also output the spherical harmonic coefficients of the geoid
    # anomaly up to the maximum degree. The default is false, so postprocess
    # will only output the geoid anomaly in grid format.
    set Also output the spherical harmonic coefficients of geoid anomaly                           = false

    # Option to also output the spherical harmonic coefficients of the surface
    # dynamic topography contribution to the maximum degree. The default is
    # false.
    set Also output the spherical harmonic coefficients of surface dynamic topography contribution = false

    # The density value above the surface boundary.
    set Density above                                                                              = 0.

    # The density value below the CMB boundary.
    set Density below                                                                              = 9900.

    # Option to include the contribution from dynamic topography on geoid. The
    # default is true.
    set Include the contributon from dynamic topography                                            = true

    # This parameter can be a random positive integer. However, the value
    # normally should not exceed the maximum degree of the initial perturbed
    # temperature field. For example, if the initial temperature uses S40RTS,
    # the maximum degree should not be larger than 40.
    set Maximum degree                                                                             = 20

    # This parameter normally is set to 2 since the perturbed gravitational
    # potential at degree 1 always vanishes in a reference frame with the
    # planetary center of mass same as the center of figure.
    set Minimum degree                                                                             = 2

    # Option to output the geoid anomaly in geographical coordinates (latitude
    # and longitude). The default is false, so postprocess will output the
    # data in geocentric coordinates (x,y,z) as normally.
    set Output data in geographical coordinates                                                    = false
  end

  subsection Global statistics
    # Whether to put every nonlinear iteration into a separate line in the
    # statistics file (if true), or to output only one line per time step that
    # contains the total number of iterations of the Stokes and advection
    # linear system solver.
    set Write statistics for each nonlinear iteration = false
  end

  subsection Gravity calculation
    # Parameter for the list of points sampling scheme: List of satellite
    # latitude coordinates.
    set List of latitude                  = 

    # Parameter for the list of points sampling scheme: List of satellite
    # longitude coordinates.
    set List of longitude                 = 

    # Parameter for the list of points sampling scheme: List of satellite
    # radius coordinates. Just specify one radius if all points values have
    # the same radius. If not, make sure there are as many radius as longitude
    # and latitude
    set List of radius                    = 

    # Parameter for the uniform distribution sampling scheme: Gravity may be
    # calculated for a sets of points along the latitude between a minimum and
    # maximum latitude.
    set Maximum latitude                  = 90

    # Parameter for the uniform distribution sampling scheme: Gravity may be
    # calculated for a sets of points along the longitude between a minimum
    # and maximum longitude.
    set Maximum longitude                 = 180.

    # Parameter for the map sampling scheme: Maximum radius can be defined in
    # or outside the model.
    set Maximum radius                    = 0.

    # Parameter for the uniform distribution sampling scheme: Gravity may be
    # calculated for a sets of points along the latitude between a minimum and
    # maximum latitude.
    set Minimum latitude                  = -90.

    # Parameter for the uniform distribution sampling scheme: Gravity may be
    # calculated for a sets of points along the longitude between a minimum
    # and maximum longitude.
    set Minimum longitude                 = -180.

    # Parameter for the map sampling scheme: Minimum radius may be defined in
    # or outside the model. Prescribe a minimum radius for a sampling coverage
    # at a specific height.
    set Minimum radius                    = 0.

    # Parameter for the fibonacci spiral sampling scheme: This specifies the
    # desired number of satellites per radius layer. The default value is 200.
    # Note that sampling becomes more uniform with increasing number of
    # satellites
    set Number points fibonacci spiral    = 200

    # Parameter for the map sampling scheme: This specifies the number of
    # points along the latitude (e.g. gravity map) between a minimum and
    # maximum latitude.
    set Number points latitude            = 1

    # Parameter for the map sampling scheme: This specifies the number of
    # points along the longitude (e.g. gravity map) between a minimum and
    # maximum longitude.
    set Number points longitude           = 1

    # Parameter for the map sampling scheme: This specifies the number of
    # points along the radius (e.g. depth profile) between a minimum and
    # maximum radius.
    set Number points radius              = 1

    # Set the precision of gravity acceleration, potential and gradients in
    # the gravity output and statistics file.
    set Precision in gravity output       = 12

    # Quadrature degree increase over the velocity element degree may be
    # required when gravity is calculated near the surface or inside the
    # model. An increase in the quadrature element adds accuracy to the
    # gravity solution from noise due to the model grid.
    set Quadrature degree increase        = 0

    # Gravity anomalies may be computed using density anomalies relative to a
    # reference density.
    set Reference density                 = 3300.

    # Choose the sampling scheme. By default, the map produces a grid of
    # equally angled points between a minimum and maximum radius, longitude,
    # and latitude. A list of points contains the specific coordinates of the
    # satellites. The fibonacci spiral sampling scheme produces a uniformly
    # distributed map on the surface of sphere defined by a minimum and/or
    # maximum radius.
    set Sampling scheme                   = map

    # The time interval between each generation of gravity output files. A
    # value of 0 indicates that output should be generated in each time step.
    # Units: years if the 'Use years in output instead of seconds' parameter
    # is set; seconds otherwise.
    set Time between gravity output       = 1e8

    # The maximum number of time steps between each generation of gravity
    # output files.
    set Time steps between gravity output = 2147483647
  end

  subsection Memory statistics
    # If set to 'true', also output the peak virtual memory usage (computed as
    # the maximum over all processors).
    set Output peak virtual memory (VmPeak) = true
  end

  subsection Particles
    # By default, every cell needs to contain particles to use this
    # interpolator plugin. If this parameter is set to true, cells are allowed
    # to have no particles, in which case the interpolator will return 0 for
    # the cell's properties.
    set Allow cells without particles = false

    # A comma separated list of file formats to be used for graphical output.
    # The list of possible output formats that can be given here is documented
    # in the appendix of the manual where the current parameter is described.
    set Data output format            = vtu

    # A comma separated list of strings which exclude all particleproperty
    # fields which contain these strings. If one of the entries is 'all', only
    # a id will be provided for every point.
    set Exclude output properties     = 

    # This parameter is used to decide which method to use to solve the
    # equation that describes the position of particles, i.e.,
    # $\frac{d}{dt}\mathbf x_k(t) = \mathbf u(\mathbf x_k(t),t)$, where $k$ is
    # an index that runs over all particles, and $\mathbf u(\mathbf x,t)$ is
    # the velocity field that results from the Stokes equations.
    # 
    # In practice, the exact velocity $\mathbf u(\mathbf x,t)$ is of course
    # not available, but only a numerical approximation $\mathbf u_h(\mathbf
    # x,t)$. Furthermore, this approximation is only available at discrete
    # time steps, $\mathbf u^n(\mathbf x)=\mathbf u(\mathbf x,t^n)$, and these
    # need to be interpolated between time steps if the integrator for the
    # equation above requires an evaluation at time points between the
    # discrete time steps. If we denote this interpolation in time by
    # $\tilde{\mathbf u}_h(\mathbf x,t)$ where $\tilde{\mathbf u}_h(\mathbf
    # x,t^n)=\mathbf u^n(\mathbf x)$, then the equation the differential
    # equation solver really tries to solve is $\frac{d}{dt}\tilde{\mathbf
    # x}_k(t) =  \tilde{\mathbf u}_h(\mathbf x_k(t),t)$.
    # 
    # As a consequence of these considerations, if you try to assess
    # convergence properties of an ODE integrator -- for example to verify
    # that the RK4 integrator converges with fourth order --, it is important
    # to recall that the integrator may not solve the equation you think it
    # solves. If, for example, we call the numerical solution of the ODE
    # $\tilde{\mathbf x}_{k,h}(t)$, then the error will typically satisfy a
    # relationship like $$  \| \tilde{\mathbf x}_k(T) - \tilde{\mathbf
    # x}_{k,h}(T) \|  \le  C(T) \Delta t^p$$ where $\Delta t$ is the time step
    # and $p$ the convergence order of the method, and $C(T)$ is a (generally
    # unknown) constant that depends on the end time $T$ at which one compares
    # the solutions. On the other hand, an analytically computed trajectory
    # would likely use the \textit{exact} velocity, and one may be tempted to
    # compute $\| \mathbf x_k(T) - \tilde{\mathbf x}_{k,h}(T) \|$, but this
    # quantity will, in the best case, only satisfy an estimate of the form $$
    # \| \mathbf x_k(T) - \tilde{\mathbf x}_{k,h}(T) \|  \le  C_1(T) \Delta
    # t^p  + C_2(T) \| \mathbf u-\mathbf u_h \|  + C_3(T) \| \mathbf
    # u_h-\tilde{\mathbf u}_h \|$$ with appropriately chosen norms for the
    # second and third term. These second and third terms typically converge
    # to zero at relatively low rates (compared to the order $p$ of the
    # integrator, which can often be chosen relatively high) in the mesh size
    # $h$ and the time step size $\\Delta t$, limiting the overall accuracy of
    # the ODE integrator.
    # 
    # Select one of the following models:
    # 
    # `euler': Explicit Euler scheme integrator, where $y_{n+1} = y_n + \Delta
    # t \, v(y_n)$. This requires only one integration substep per timestep.
    # 
    # `rk2': Second Order Runge Kutta integrator $y_{n+1} = y_n + \Delta t\,
    # v(t_{n+1/2}, y_{n} + \frac{1}{2} k_1)$ where $k_1 = \Delta t\, v(t_{n},
    # y_{n})$
    # 
    # `rk4': Runge Kutta fourth order integrator, where $y_{n+1} = y_n +
    # \frac{1}{6} k_1 + \frac{1}{3} k_2 + \frac{1}{3} k_3 + \frac{1}{6} k_4$
    # and $k_1$, $k_2$, $k_3$, $k_4$ are defined as usual.
    set Integration scheme            = rk2

    # Select one of the following models:
    # 
    # `bilinear least squares': Interpolates particle properties onto a vector
    # of points using a bilinear least squares method. Note that deal.II must
    # be configured with BLAS and LAPACK to support this operation.
    # 
    # `cell average': Return the arithmetic average of all particle properties
    # in the given cell.
    # 
    # `harmonic average': Return the harmonic average of all particle
    # properties in the given cell. If the cell contains no particles, return
    # the harmonic average of the properties in the neighboring cells.
    # 
    # `nearest neighbor': Return the properties of the nearest neighboring
    # particle in the current cell, or nearest particle in nearest neighboring
    # cell if current cell is empty.
    # 
    # `quadratic least squares': Interpolates particle properties onto a
    # vector of points using a quadratic least squares method. Note that
    # deal.II must be configured with BLAS/LAPACK.
    set Interpolation scheme          = cell average

    # A comma separated list of particle properties that should be tracked. By
    # default none is selected, which means only position, velocity and id of
    # the particles are output.
    # 
    # The following properties are available:
    # 
    # `composition': Implementation of a plugin in which the particle property
    # is defined by the compositional fields in the model. This can be used to
    # track solid compositionevolution over time.
    # 
    # `elastic stress': A plugin in which the particle property tensor is
    # defined as the total elastic stress a particle has accumulated. See the
    # viscoelastic material model documentation for more detailed information.
    # 
    # `function': Implementation of a model in which the particle property is
    # set by evaluating an explicit function at the initial position of each
    # particle. The function is defined in the parameters in section
    # ``Particles|Function''. The format of these functions follows the syntax
    # understood by the muparser library, see
    # Section~\ref{sec:muparser-format}.
    # 
    # `initial composition': Implementation of a plugin in which the particle
    # property is given as the initial composition at the particle's initial
    # position. The particle gets as many properties as there are
    # compositional fields.
    # 
    # `initial position': Implementation of a plugin in which the particle
    # property is given as the initial position of the particle. This property
    # is vector-valued with as many components as there are space dimensions.
    # In practice, it is often most useful to only visualize one of the
    # components of this vector, or the magnitude of the vector. For example,
    # in a spherical mantle simulation, the magnitude of this property equals
    # the starting radius of a particle, and is thereby indicative of which
    # part of the mantle a particle comes from.
    # 
    # `integrated strain': A plugin in which the particle property tensor is
    # defined as the deformation gradient tensor $\mathbf F$ this particle has
    # experienced. $\mathbf F$ can be polar-decomposed into the left
    # stretching tensor $\mathbf L$ (the finite strain we are interested in),
    # and the rotation tensor $\mathbf Q$. See the corresponding cookbook in
    # the manual for more detailed information.
    # 
    # `integrated strain invariant': A plugin in which the particle property
    # is defined as the finite strain invariant ($\varepsilon_{ii}$). This
    # property is calculated with the timestep ($dt$) and the second invariant
    # of the deviatoric strain rate tensor ($\dot{\varepsilon}_{ii}$), where
    # the value at time step $n$ is $\varepsilon_{ii}^{n} =
    # \varepsilon_{ii}^{n-1} + dt\dot{\varepsilon}_{ii}$.
    # 
    # `melt particle': Implementation of a plugin in which the particle
    # property is defined as presence of melt above a threshold, which can be
    # set as an input parameter. This property is set to 0 if melt is not
    # present and set to 1 if melt is present.
    # 
    # `pT path': Implementation of a plugin in which the particle property is
    # defined as the current pressure and temperature at this position. This
    # can be used to generate pressure-temperature paths of material points
    # over time.
    # 
    # `position': Implementation of a plugin in which the particle property is
    # defined as the current position.
    # 
    # `reference position': Implementation of a plugin in which the particle
    # property is defined as the current reference position.
    # 
    # `velocity': Implementation of a plugin in which the particle property is
    # defined as the recent velocity at this position.
    # 
    # `viscoplastic strain invariants': A plugin that calculates the finite
    # strain invariant a particle has experienced and assigns it to either the
    # plastic and/or viscous strain field based on whether the material is
    # plastically yielding, or the total strain field used in the visco
    # plastic material model. The implementation of this property is
    # equivalent to the implementation for compositional fields that is
    # located in the plugin in
    # \texttt{benchmarks/buiter\_et\_al\_2008\_jgr/plugin/},and is effectively
    # the same as what the visco plastic material model uses for compositional
    # fields.
    set List of particle properties   = 

    # Strategy that is used to balance the computational load across
    # processors for adaptive meshes.
    set Load balancing strategy       = repartition

    # Upper limit for particle number per cell. This limit is useful for
    # adaptive meshes to prevent coarse cells from slowing down the whole
    # model. It will be checked and enforced after mesh refinement, after MPI
    # transfer of particles and after particle movement. If there are
    # \texttt{n\_number\_of\_particles} $>$ \texttt{max\_particles\_per\_cell}
    # particles in one cell then \texttt{n\_number\_of\_particles} -
    # \texttt{max\_particles\_per\_cell} particles in this cell are randomly
    # chosen and destroyed.
    set Maximum particles per cell    = 100

    # Lower limit for particle number per cell. This limit is useful for
    # adaptive meshes to prevent fine cells from being empty of particles. It
    # will be checked and enforced after mesh refinement and after particle
    # movement. If there are \texttt{n\_number\_of\_particles} $<$
    # \texttt{min\_particles\_per\_cell} particles in one cell then
    # \texttt{min\_particles\_per\_cell} - \texttt{n\_number\_of\_particles}
    # particles are generated and randomly placed in this cell. If the
    # particles carry properties the individual property plugins control how
    # the properties of the new particles are initialized.
    set Minimum particles per cell    = 0

    # VTU file output supports grouping files from several CPUs into a given
    # number of files using MPI I/O when writing on a parallel filesystem.
    # Select 0 for no grouping. This will disable parallel file output and
    # instead write one file per processor. A value of 1 will generate one big
    # file containing the whole solution, while a larger value will create
    # that many files (at most as many as there are MPI ranks).
    set Number of grouped files       = 16

    # Total number of particles to create (not per processor or per element).
    # The number is parsed as a floating point number (so that one can
    # specify, for example, '1e4' particles) but it is interpreted as an
    # integer, of course.
    set Number of particles           = 1000

    # Select one of the following models:
    # 
    # `ascii file': Generates a distribution of particles from coordinates
    # specified in an Ascii data file. The file format is a simple text file,
    # with as many columns as spatial dimensions and as many lines as
    # particles to be generated. Initial comment lines starting with `#' will
    # be discarded. Note that this plugin always generates as many particles
    # as there are coordinates in the data file, the
    # ``Postprocess/Particles/Number of particles'' parameter has no effect on
    # this plugin. All of the values that define this generator are read from
    # a section ``Postprocess/Particles/Generator/Ascii file'' in the input
    # file, see
    # Section~\ref{parameters:Postprocess/Particles/Generator/Ascii_20file}.
    # 
    # `probability density function': Generate a random distribution of
    # particles over the entire simulation domain. The probability density is
    # prescribed in the form of a user-prescribed function. The format of this
    # function follows the syntax understood by the muparser library, see
    # Section~\ref{sec:muparser-format}. The return value of the function is
    # always checked to be a non-negative probability density but it can be
    # zero in parts of the domain.
    # 
    # `quadrature points': Generates particles at the quadrature points of
    # each active cell of the triangulation. Here, Gauss quadrature of degree
    # (velocity\_degree + 1), is used similarly to the assembly of Stokes
    # matrix.
    # 
    # `random uniform': Generates a random uniform distribution of particles
    # over the entire simulation domain.
    # 
    # `reference cell': Generates a uniform distribution of particles per cell
    # and spatial direction in the unit cell and transforms each of the
    # particles back to real region in the model domain. Uniform here means
    # the particles will be generated with an equal spacing in each spatial
    # dimension
    # 
    # `uniform box': Generate a uniform distribution of particles over a
    # rectangular domain in 2D or 3D. Uniform here means the particles will be
    # generated with an equal spacing in each spatial dimension. Note that in
    # order to produce a regular distribution the number of generated
    # particles might not exactly match the one specified in the input file.
    # 
    # `uniform radial': Generate a uniform distribution of particles over a
    # spherical domain in 2D or 3D. Uniform here means the particles will be
    # generated with an equal spacing in each spherical spatial dimension,
    # i.e., the particles are created at positions that increase linearly with
    # equal spacing in radius, colatitude and longitude around a certain
    # center point. Note that in order to produce a regular distribution the
    # number of generated particles might not exactly match the one specified
    # in the input file.
    set Particle generator name       = random uniform

    # Weight that is associated with the computational load of a single
    # particle. The sum of particle weights will be added to the sum of cell
    # weights to determine the partitioning of the mesh if the `repartition'
    # particle load balancing strategy is selected. The optimal weight depends
    # on the used integrator and particle properties. In general for a more
    # expensive integrator and more expensive properties a larger particle
    # weight is recommended. Before adding the weights of particles, each cell
    # already carries a weight of 1000 to account for the cost of field-based
    # computations.
    set Particle weight               = 10

    # On large clusters it can be advantageous to first write the output to a
    # temporary file on a local file system and later move this file to a
    # network file system. If this variable is set to a non-empty string it
    # will be interpreted as a temporary storage location.
    set Temporary output location     = 

    # The time interval between each generation of output files. A value of
    # zero indicates that output should be generated every time step.
    # 
    # Units: years if the 'Use years in output instead of seconds' parameter
    # is set; seconds otherwise.
    set Time between data output      = 1e8

    # Some particle interpolation algorithms require knowledge about particles
    # in neighboring cells. To allow this, particles in ghost cells need to be
    # exchanged between the processes neighboring this cell. This parameter
    # determines whether this transport is happening.
    set Update ghost particles        = false

    # File operations can potentially take a long time, blocking the progress
    # of the rest of the model run. Setting this variable to `true' moves this
    # process into a background thread, while the rest of the model
    # continues.
    set Write in background thread    = false


    subsection Function
      # Sometimes it is convenient to use symbolic constants in the expression
      # that describes the function, rather than having to use its numeric
      # value everywhere the constant appears. These values can be defined
      # using this parameter, in the form `var1=value1, var2=value2, ...'.
      # 
      # A typical example would be to set this runtime parameter to
      # `pi=3.1415926536' and then use `pi' in the expression of the actual
      # formula. (That said, for convenience this class actually defines both
      # `pi' and `Pi' by default, but you get the idea.)
      set Function constants   = 

      # The formula that denotes the function you want to evaluate for
      # particular values of the independent variables. This expression may
      # contain any of the usual operations such as addition or
      # multiplication, as well as all of the common functions such as `sin'
      # or `cos'. In addition, it may contain expressions like `if(x>0, 1,
      # -1)' where the expression evaluates to the second argument if the
      # first argument is true, and to the third argument otherwise. For a
      # full overview of possible expressions accepted see the documentation
      # of the muparser library at http://muparser.beltoforion.de/.
      # 
      # If the function you are describing represents a vector-valued function
      # with multiple components, then separate the expressions for individual
      # components by a semicolon.
      set Function expression  = 0

      # The number of function components where each component is described by
      # a function expression delimited by a ';'.
      set Number of components = 1

      # The names of the variables as they will be used in the function,
      # separated by commas. By default, the names of variables at which the
      # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
      # (in 3d) for spatial coordinates and `t' for time. You can then use
      # these variable names in your function expression and they will be
      # replaced by the values of these variables at which the function is
      # currently evaluated. However, you can also choose a different set of
      # names for the independent variables at which to evaluate your function
      # expression. For example, if you work in spherical coordinates, you may
      # wish to set this input parameter to `r,phi,theta,t' and then use these
      # variable names in your function expression.
      set Variable names       = x,y,t
    end

    subsection Generator
      subsection Ascii file
        # The name of a directory that contains the particle data. This path
        # may either be absolute (if starting with a '/') or relative to the
        # current directory. The path may also include the special text
        # '$ASPECT_SOURCE_DIR' which will be interpreted as the path in which
        # the ASPECT source files were located when ASPECT was compiled. This
        # interpretation allows, for example, to reference files located in
        # the `data/' subdirectory of ASPECT.
        set Data directory = $ASPECT_SOURCE_DIR/data/particle/generator/ascii/

        # The name of the particle file.
        set Data file name = particle.dat
      end

      subsection Probability density function
        # Sometimes it is convenient to use symbolic constants in the
        # expression that describes the function, rather than having to use
        # its numeric value everywhere the constant appears. These values can
        # be defined using this parameter, in the form `var1=value1,
        # var2=value2, ...'.
        # 
        # A typical example would be to set this runtime parameter to
        # `pi=3.1415926536' and then use `pi' in the expression of the actual
        # formula. (That said, for convenience this class actually defines
        # both `pi' and `Pi' by default, but you get the idea.)
        set Function constants    = 

        # The formula that denotes the function you want to evaluate for
        # particular values of the independent variables. This expression may
        # contain any of the usual operations such as addition or
        # multiplication, as well as all of the common functions such as `sin'
        # or `cos'. In addition, it may contain expressions like `if(x>0, 1,
        # -1)' where the expression evaluates to the second argument if the
        # first argument is true, and to the third argument otherwise. For a
        # full overview of possible expressions accepted see the documentation
        # of the muparser library at http://muparser.beltoforion.de/.
        # 
        # If the function you are describing represents a vector-valued
        # function with multiple components, then separate the expressions for
        # individual components by a semicolon.
        set Function expression   = 0

        # If true, particle numbers per cell are calculated randomly according
        # to their respective probability density. This means particle numbers
        # per cell can deviate statistically from the integral of the
        # probability density. If false, first determine how many particles
        # each cell should have based on the integral of the density over each
        # of the cells, and then once we know how many particles we want on
        # each cell, choose their locations randomly within each cell.
        set Random cell selection = true

        # The seed for the random number generator that controls the particle
        # generation. Keep constant to generate identical particle
        # distributions in subsequent model runs. Change to get a different
        # distribution. In parallel computations the seed is further modified
        # on each process to ensure different particle patterns on different
        # processes. Note that the number of particles per processor is not
        # affected by the seed.
        set Random number seed    = 5432

        # The names of the variables as they will be used in the function,
        # separated by commas. By default, the names of variables at which the
        # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z'
        # (in 3d) for spatial coordinates and `t' for time. You can then use
        # these variable names in your function expression and they will be
        # replaced by the values of these variables at which the function is
        # currently evaluated. However, you can also choose a different set of
        # names for the independent variables at which to evaluate your
        # function expression. For example, if you work in spherical
        # coordinates, you may wish to set this input parameter to
        # `r,phi,theta,t' and then use these variable names in your function
        # expression.
        set Variable names        = x,y,t
      end

      subsection Reference cell
        # List of number of particles to create per cell and spatial
        # dimension. The size of the list is the number of spatial dimensions.
        # If only one value is given, then each spatial dimension is set to
        # the same value. The list of numbers are parsed as a floating point
        # number (so that one can specify, for example, '1e4' particles) but
        # it is interpreted as an integer, of course.
        set Number of particles per cell per direction = 2
      end

      subsection Uniform box
        # Maximum x coordinate for the region of particles.
        set Maximum x = 1.

        # Maximum y coordinate for the region of particles.
        set Maximum y = 1.

        # Maximum z coordinate for the region of particles.
        set Maximum z = 1.

        # Minimum x coordinate for the region of particles.
        set Minimum x = 0.

        # Minimum y coordinate for the region of particles.
        set Minimum y = 0.

        # Minimum z coordinate for the region of particles.
        set Minimum z = 0.
      end

      subsection Uniform radial
        # x coordinate for the center of the spherical region, where particles
        # are generated.
        set Center x          = 0.

        # y coordinate for the center of the spherical region, where particles
        # are generated.
        set Center y          = 0.

        # z coordinate for the center of the spherical region, where particles
        # are generated.
        set Center z          = 0.

        # Maximum latitude coordinate for the region of particles in degrees.
        # Measured from the center position, and from the north pole.
        set Maximum latitude  = 180.

        # Maximum longitude coordinate for the region of particles in degrees.
        # Measured from the center position.
        set Maximum longitude = 360.

        # Maximum radial coordinate for the region of particles. Measured from
        # the center position.
        set Maximum radius    = 1.

        # Minimum latitude coordinate for the region of particles in degrees.
        # Measured from the center position, and from the north pole.
        set Minimum latitude  = 0.

        # Minimum longitude coordinate for the region of particles in degrees.
        # Measured from the center position.
        set Minimum longitude = 0.

        # Minimum radial coordinate for the region of particles. Measured from
        # the center position.
        set Minimum radius    = 0.

        # The number of radial shells of particles that will be generated
        # around the central point.
        set Radial layers     = 1
      end

    end

    subsection Interpolator
      subsection Bilinear least squares
        # The maximum global particle property values that will be used as a
        # limiter for the bilinear least squares interpolation. The number of
        # the input 'Global particle property maximum' values separated by ','
        # has to be the same as the number of particle properties.
        set Global particle property maximum = 1.7976931348623157e+308

        # The minimum global particle property that will be used as a limiter
        # for the bilinear least squares interpolation. The number of the
        # input 'Global particle property minimum' values separated by ',' has
        # to be the same as the number of particle properties.
        set Global particle property minimum = -1.7976931348623157e+308

        # Whether to apply a global particle property limiting scheme to the
        # interpolated particle properties.
        set Use limiter                      = false
      end

      subsection Quadratic least squares
        # The maximum global particle property values that will be used as a
        # limiter for the quadratic least squares interpolation. The number of
        # the input 'Global particle property maximum' values separated by ','
        # has to be the same as the number of particle properties.
        set Global particle property maximum = 1.7976931348623157e+308

        # The minimum global particle property that will be used as a limiter
        # for the quadratic least squares interpolation. The number of the
        # input 'Global particle property minimum' values separated by ',' has
        # to be the same as the number of particle properties.
        set Global particle property minimum = -1.7976931348623157e+308

        # Whether to apply a global particle property limiting scheme to the
        # interpolated particle properties.
        set Use limiter                      = false
      end

    end

    subsection Melt particle
      # The minimum porosity that has to be present at the position of a
      # particle for it to be considered a melt particle (in the sense that
      # the melt presence property is set to 1).
      set Threshold for melt presence = 1e-3
    end

  end

  subsection Point values
    # The list of points at which the solution should be evaluated. Points
    # need to be separated by semicolons, and coordinates of each point need
    # to be separated by commas.
    set Evaluation points                = 

    # The time interval between each generation of point values output. A
    # value of zero indicates that output should be generated in each time
    # step. Units: years if the 'Use years in output instead of seconds'
    # parameter is set; seconds otherwise.
    set Time between point values output = 0.

    # Whether or not the Evaluation points are specified in the natural
    # coordinates of the geometry model, e.g. radius, lon, lat for the chunk
    # model. Currently, natural coordinates for the spherical shell and sphere
    # geometries are not supported.
    set Use natural coordinates          = false
  end

  subsection Rotation statistics
    # Whether to write the full moment of inertia tensor into the statistics
    # output instead of its norm for the current rotation axis. This is a
    # second-order symmetric tensor with 6 components in 3D. In 2D this option
    # has no effect, because the rotation axis is fixed and thus the moment of
    # inertia is always a scalar.
    set Output full moment of inertia tensor = false

    # Whether to use a constant density of one for the computation of the
    # angular momentum and moment of inertia. This is an approximation that
    # assumes that the 'volumetric' rotation is equal to the 'mass' rotation.
    # If this parameter is true this postprocessor computes 'net rotation'
    # instead of 'angular momentum'.
    set Use constant density of one          = false
  end

  subsection Topography
    # Whether or not to write topography to a text file named named
    # 'topography.NNNNN' in the output directory
    set Output to file           = false

    # The time interval between each generation of text output files. A value
    # of zero indicates that output should be generated in each time step.
    # Units: years if the 'Use years in output instead of seconds' parameter
    # is set; seconds otherwise.
    set Time between text output = 0.
  end

  subsection Visualization
    # deal.II offers the possibility to filter duplicate vertices for HDF5
    # output files. This merges the vertices of adjacent cells and therefore
    # saves disk space, but misrepresents discontinuous output properties.
    # Activating this function reduces the disk space by about a factor of
    # $2^{dim}$ for HDF5 output, and currently has no effect on other output
    # formats. \note{\textbf{Warning:} Setting this flag to true will result
    # in visualization output that does not accurately represent discontinuous
    # fields. This may be because you are using a discontinuous finite element
    # for the pressure, temperature, or compositional variables, or because
    # you use a visualization postprocessor that outputs quantities as
    # discontinuous fields (e.g., the strain rate, viscosity, etc.). These
    # will then all be visualized as \textit{continuous} quantities even
    # though, internally, \aspect{} considers them as discontinuous fields.}
    set Filter output                       = false

    # deal.II offers the possibility to linearly interpolate output fields of
    # higher order elements to a finer resolution. This somewhat compensates
    # the fact that most visualization software only offers linear
    # interpolation between grid points and therefore the output file is a
    # very coarse representation of the actual solution field. Activating this
    # option increases the spatial resolution in each dimension by a factor
    # equal to the polynomial degree used for the velocity finite element
    # (usually 2). In other words, instead of showing one quadrilateral or
    # hexahedron in the visualization per cell on which \aspect{} computes, it
    # shows multiple (for quadratic elements, it will describe each cell of
    # the mesh on which we compute as $2\times 2$ or $2\times 2\times 2$ cells
    # in 2d and 3d, respectively; correspondingly more subdivisions are used
    # if you use cubic, quartic, or even higher order elements for the
    # velocity).
    # 
    # The effect of using this option can be seen in the following picture
    # showing a variation of the output produced with the input files from
    # Section~\ref{sec:shell-simple-2d}:
    # 
    # \begin{center}
    # \includegraphics[width=0.5\textwidth]{viz/parameters/build-patches}\end{center}Here,
    # the left picture shows one visualization cell per computational cell
    # (i.e., the option is switched off), and the right picture shows the same
    # simulation with the option switched on (which is the default). The
    # images show the same data, demonstrating that interpolating the solution
    # onto bilinear shape functions as is commonly done in visualizing data
    # loses information.
    # 
    # Of course, activating this option also greatly increases the amount of
    # data \aspect{} will write to disk: approximately by a factor of 4 in 2d,
    # and a factor of 8 in 3d, when using quadratic elements for the velocity,
    # and correspondingly more for even higher order elements.
    set Interpolate output                  = false                  # default: true

    # A comma separated list of visualization objects that should be run
    # whenever writing graphical output. By default, the graphical output
    # files will always contain the primary variables velocity, pressure, and
    # temperature. However, one frequently wants to also visualize derived
    # quantities, such as the thermodynamic phase that corresponds to a given
    # temperature-pressure value, or the corresponding seismic wave speeds.
    # The visualization objects do exactly this: they compute such derived
    # quantities and place them into the output file. The current parameter is
    # the place where you decide which of these additional output variables
    # you want to have in your output file.
    # 
    # The following postprocessors are available:
    # 
    # `ISA rotation timescale': A visualization output object that generates
    # output showing the timescale for the rotation of grains toward the
    # infinite strain axis. Kaminski and Ribe (2002, Gcubed) call this
    # quantity $\tau_{ISA}$ and define it as $\tau_{ISA} \approx
    # \frac{1}{\dot{\epsilon}}$ where $\dot{\epsilon}$ is the largest
    # eigenvalue of the strain rate tensor. It can be used, along with the
    # grain lag angle $\Theta$, to calculate the grain orientation lag
    # parameter.
    # 
    # `Vp anomaly': A visualization output object that generates output
    # showing the percentage anomaly in the seismic compressional wave speed
    # $V_p$ as a spatially variable function with one value per cell. This
    # anomaly is either shown as a percentage anomaly relative to the
    # reference profile given by adiabatic conditions (with the compositions
    # given by the current composition, such that the reference could
    # potentially change through time), or as a percentage change relative to
    # the laterally averaged velocity at the depth of the cell. This velocity
    # is calculated by linear interpolation between average values calculated
    # within equally thick depth slices. The number of depth slices in the
    # domain is user-defined. Typically, the best results will be obtained if
    # the number of depth slices is balanced between being large enough to
    # capture step changes in velocities, but small enough to maintain a
    # reasonable number of evaluation points per slice. Bear in mind that
    # lateral averaging subsamples the finite element mesh. Note that this
    # plugin requires a material model that provides seismic velocities.
    # 
    # `Vs anomaly': A visualization output object that generates output
    # showing the percentage anomaly in the seismic shear wave speed $V_s$ as
    # a spatially variable function with one value per cell. This anomaly is
    # either shown as a percentage anomaly relative to the reference profile
    # given by adiabatic conditions (with the compositions given by the
    # current composition, such that the reference could potentially change
    # through time), or as a percentage change relative to the laterally
    # averaged velocity at the depth of the cell. This velocity is calculated
    # by linear interpolation between average values calculated within equally
    # thick depth slices. The number of depth slices in the domain is
    # user-defined. Typically, the best results will be obtained if the number
    # of depth slices is balanced between being large enough to capture step
    # changes in velocities, but small enough to maintain a reasonable number
    # of evaluation points per slice. Bear in mind that lateral averaging
    # subsamples the finite element mesh. Note that this plugin requires a
    # material model that provides seismic velocities.
    # 
    # `adiabat': A visualization output object that generates adiabatic
    # temperature, pressure, density, and density derivative as produced by
    # AdiabaticConditions.
    # 
    # `artificial viscosity': A visualization output object that generates
    # output showing the value of the artificial viscosity on each cell.
    # 
    # `artificial viscosity composition': A visualization output object that
    # generates output showing the value of the artificial viscosity for a
    # compositional field on each cell.
    # 
    # `boundary indicators': A visualization output object that generates
    # output about the used boundary indicators. In a loop over the active
    # cells, if a cell lies at a domain boundary, the boundary indicator of
    # the face along the boundary is requested. In case the cell does not lie
    # along any domain boundary, the cell is assigned the value of the largest
    # used boundary indicator plus one. When a cell is situated in one of the
    # corners of the domain, multiple faces will have a boundary indicator.
    # This postprocessor returns the value of the first face along a boundary
    # that is encountered in a loop over all the faces.
    # 
    # `boundary velocity residual': A visualization output object that
    # generates output for the velocity residual at the top surface. The
    # residual is computed at each point at the surface as the difference
    # between the modeled velocities and the input data velocities for each
    # vector component. The user has an option to choose the input data as
    # ascii data files (e.g. GPS velocities) with columns in the same format
    # as described for the 'ascii data' initial temperature plugin or a
    # velocity field computed from the GPlates program as described in the
    # gplates boundary velocity plugin.
    # 
    # `compositional vector': A visualization output object that outputs
    # vectors whose components are derived from compositional fields. Input
    # parameters for this postprocessor are defined in section
    # Postprocess/Visualization/Compositional fields as vectors
    # 
    # `depth': A visualization output postprocessor that outputs the depth for
    # all points inside the domain, as determined by the geometry model.
    # 
    # `dynamic topography': A visualization output object that generates
    # output for the dynamic topography at the top and bottom of the model
    # space. The approach to determine the dynamic topography requires us to
    # compute the stress tensor and evaluate the component of it in the
    # direction in which gravity acts. In other words, we compute
    # $\sigma_{rr}={\hat g}^T(2 \eta \varepsilon(\mathbf u)-\frac 13
    # (\textrm{div}\;\mathbf u)I)\hat g - p_d$ where $\hat g = \mathbf
    # g/\|\mathbf g\|$ is the direction of the gravity vector $\mathbf g$ and
    # $p_d=p-p_a$ is the dynamic pressure computed by subtracting the
    # adiabatic pressure $p_a$ from the total pressure $p$ computed as part of
    # the Stokes solve. From this, the dynamic topography is computed using
    # the formula $h=\frac{\sigma_{rr}}{(\mathbf g \cdot \mathbf n)  \rho}$
    # where $\rho$ is the density at the cell center. For the bottom surface
    # we chose the convection that positive values are up (out) and negative
    # values are in (down), analogous to the deformation of the upper surface.
    # Note that this implementation takes the direction of gravity into
    # account, which means that reversing the flow in backward advection
    # calculations will not reverse the instantaneous topography because the
    # reverse flow will be divided by the reverse surface gravity.
    # 
    # Strictly speaking, the dynamic topography is of course a quantity that
    # is only of interest at the surface. However, we compute it everywhere to
    # make things fit into the framework within which we produce data for
    # visualization. You probably only want to visualize whatever data this
    # postprocessor generates at the surface of your domain and simply ignore
    # the rest of the data generated.
    # 
    # Alternatively, consider using the "surface dynamic topography"
    # visualization postprocessor to only output the dynamic topography at the
    # boundary of the domain.
    # 
    # `error indicator': A visualization output object that generates output
    # showing the estimated error or other mesh refinement indicator as a
    # spatially variable function with one value per cell.
    # 
    # `geoid': Visualization for the geoid solution. The geoid is given by the
    # equivalent water column height due to a gravity perturbation. Units:
    # \si{\meter}.
    # 
    # `grain lag angle': A visualization output object that generates output
    # showing the angle between the ~infinite strain axis and the flow
    # velocity. Kaminski and Ribe (2002, Gcubed) call this quantity $\Theta$
    # and define it as $\Theta = \cos^{-1}(\hat{u}\cdot\hat{e})$  where
    # $\hat{u}=\vec{u}/|{u}|$, $\vec{u}$ is the local flow velocity, and
    # $\hat{e}$ is the local infinite strain axis, which we calculate as the
    # first eigenvector of the 'left stretch' tensor. $\Theta$ can be used to
    # calculate the grain orientation lag parameter.
    # 
    # `gravity': A visualization output object that outputs the gravity
    # vector.
    # 
    # `heat flux map': A visualization output object that generates output for
    # the heat flux density across the top and bottom boundary in outward
    # direction. The heat flux is computed as sum of advective heat flux and
    # conductive heat flux through Neumann boundaries, both computed as
    # integral over the boundary area, and conductive heat flux through
    # Dirichlet boundaries, which is computed using the consistent boundary
    # flux method as described in ``Gresho, Lee, Sani, Maslanik, Eaton (1987).
    # The consistent Galerkin FEM for computing derived boundary quantities in
    # thermal and or fluids problems. International Journal for Numerical
    # Methods in Fluids, 7(4), 371-394.'' If only conductive heat flux through
    # Dirichlet boundaries is of interest, the postprocessor can produce
    # output of higher resolution by evaluating the CBF solution vector
    # point-wise instead of computing cell-wise averaged values.
    # 
    # `heating': A visualization output object that generates output for all
    # the heating terms used in the energy equation.
    # 
    # `material properties': A visualization output object that generates
    # output for the material properties given by the material model.There are
    # a number of other visualization postprocessors that offer to write
    # individual material properties. However, they all individually have to
    # evaluate the material model. This is inefficient if one wants to output
    # more than just one or two of the fields provided by the material model.
    # The current postprocessor allows to output a (potentially large) subset
    # of all of the information provided by material models at once, with just
    # a single material model evaluation per output point.
    # 
    # `maximum horizontal compressive stress': A plugin that computes the
    # direction and magnitude of the maximum horizontal component of the
    # compressive stress as a vector field. The direction of this vector can
    # often be used to visualize the principal mode of deformation (e.g., at
    # normal faults or extensional margins) and can be correlated with seismic
    # anisotropy. Recall that the \textit{compressive} stress is simply the
    # negative stress, $\sigma_c=-\sigma=-\left[     2\eta
    # (\varepsilon(\mathbf u)             - \frac 13 (\nabla \cdot \mathbf u)
    # I)     + pI\right]$.
    # 
    # Following \cite{LundTownend07}, we define the maximum horizontal stress
    # direction as that \textit{horizontal} direction $\mathbf n$ that
    # maximizes $\mathbf n^T \sigma_c \mathbf n$. We call a vector
    # \textit{horizontal} if it is perpendicular to the gravity vector
    # $\mathbf g$.
    # 
    # In two space dimensions, $\mathbf n$ is simply a vector that is
    # horizontal (we choose one of the two possible choices). This direction
    # is then scaled by the size of the horizontal stress in this direction,
    # i.e., the plugin outputs the vector $\mathbf w = (\mathbf n^T \sigma_c
    # \mathbf n) \; \mathbf n$.
    # 
    # In three space dimensions, given two horizontal, perpendicular, unit
    # length, but otherwise arbitrarily chosen vectors $\mathbf u,\mathbf v$,
    # we can express $\mathbf n = (\cos \alpha)\mathbf u + (\sin\alpha)\mathbf
    # v$ where $\alpha$ maximizes the expression \begin{align*}  f(\alpha) =
    # \mathbf n^T \sigma_c \mathbf n  = (\mathbf u^T \sigma_c \mathbf
    # u)(\cos\alpha)^2    +2(\mathbf u^T \sigma_c \mathbf
    # v)(\cos\alpha)(\sin\alpha)    +(\mathbf v^T \sigma_c \mathbf
    # v)(\sin\alpha)^2.\end{align*}
    # 
    # The maximum of $f(\alpha)$ is attained where $f'(\alpha)=0$. Evaluating
    # the derivative and using trigonometric identities, one finds that
    # $\alpha$ has to satisfy the equation \begin{align*}  \tan(2\alpha) =
    # \frac{2.0\mathbf u^T \sigma_c \mathbf v}
    # {\mathbf u^T \sigma_c \mathbf u                            - \mathbf v^T
    # \sigma_c \mathbf v}.\end{align*}Since the transform
    # $\alpha\mapsto\alpha+\pi$ flips the direction of $\mathbf n$, we only
    # need to seek a solution to this equation in the interval
    # $\alpha\in[0,\pi)$. These are given by $\alpha_1=\frac 12 \arctan
    # \frac{\mathbf u^T \sigma_c \mathbf v}{\mathbf u^T \sigma_c \mathbf u -
    # \mathbf v^T \sigma_c \mathbf v}$ and $\alpha_2=\alpha_1+\frac{\pi}{2}$,
    # one of which will correspond to a minimum and the other to a maximum of
    # $f(\alpha)$. One checks the sign of $f''(\alpha)=-2(\mathbf u^T \sigma_c
    # \mathbf u - \mathbf v^T \sigma_c \mathbf v)\cos(2\alpha) - 2 (\mathbf
    # u^T \sigma_c \mathbf v) \sin(2\alpha)$ for each of these to determine
    # the $\alpha$ that maximizes $f(\alpha)$, and from this immediately
    # arrives at the correct form for the maximum horizontal stress $\mathbf
    # n$.
    # 
    # The description above computes a 3d \textit{direction} vector $\mathbf
    # n$. If one were to scale this vector the same way as done in 2d, i.e.,
    # with the magnitude of the stress in this direction, one will typically
    # get vectors whose length is principally determined by the hydrostatic
    # pressure at a given location simply because the hydrostatic pressure is
    # the largest component of the overall stress. On the other hand, the
    # hydrostatic pressure does not determine any principal direction because
    # it is an isotropic, anti-compressive force. As a consequence, there are
    # often points in simulations (e.g., at the center of convection rolls)
    # where the stress has no dominant horizontal direction, and the algorithm
    # above will then in essence choose a random direction because the stress
    # is approximately equal in all horizontal directions. If one scaled the
    # output by the magnitude of the stress in this direction (i.e.,
    # approximately equal to the hydrostatic pressure at this point), one
    # would get randomly oriented vectors at these locations with significant
    # lengths.
    # 
    # To avoid this problem, we scale the maximal horizontal compressive
    # stress direction $\mathbf n$ by the \textit{difference} between the
    # stress in the maximal and minimal horizontal stress directions. In other
    # words, let $\mathbf n_\perp=(\sin \alpha)\mathbf u - (\cos\alpha)\mathbf
    # v$ be the horizontal direction perpendicular to $\mathbf n$, then this
    # plugin outputs the vector quantity $\mathbf w = (\mathbf n^T \sigma_c
    # \mathbf n                -\mathbf n^T_\perp \sigma_c \mathbf n_\perp)
    # \; \mathbf n$. In other words, the length of the vector produced
    # indicates \textit{how dominant} the direction of maximal horizontal
    # compressive strength is.
    # 
    # Fig.~\ref{fig:max-horizontal-compressive-stress} shows a simple example
    # for this kind of visualization in 3d.
    # 
    # \begin{figure}  \includegraphics[width=0.3\textwidth]
    # {viz/plugins/maximum_horizontal_compressive_stress/temperature.png}
    # \hfill  \includegraphics[width=0.3\textwidth]
    # {viz/plugins/maximum_horizontal_compressive_stress/velocity.png}  \hfill
    # \includegraphics[width=0.3\textwidth]
    # {viz/plugins/maximum_horizontal_compressive_stress/horizontal-stress.png}
    # \caption{\it Illustration of the `maximum horizontal     compressive
    # stress' visualization plugin. The left     figure shows a ridge-like
    # temperature anomaly. Together     with no-slip boundary along all six
    # boundaries, this     results in two convection rolls (center). The
    # maximal     horizontal compressive strength at the bottom center     of
    # the domain is perpendicular to the ridge because     the flow comes
    # together there from the left and right,     yielding a compressive force
    # in left-right direction.     At the top of the model, the flow separates
    # outward,     leading to a \textit{negative} compressive stress     in
    # left-right direction; because there is no flow     in front-back
    # direction, the compressive strength     in front-back direction is zero,
    # making the along-ridge     direction the dominant one. At the center of
    # the     convection rolls, both horizontal directions yield     the same
    # stress; the plugin therefore chooses an     essentially arbitrary
    # horizontal vector, but then     uses a zero magnitude given that the
    # difference     between the maximal and minimal horizontal stress     is
    # zero at these points.}
    # \label{fig:max-horizontal-compressive-stress}\end{figure}
    # 
    # `melt fraction': A visualization output object that generates output for
    # the melt fraction at the temperature and pressure of the current point.
    # If the material model computes a melt fraction, this is the quantity
    # that will be visualized. Otherwise, a specific parametrization for batch
    # melting (as described in the following) will be used. It does not take
    # into account latent heat. If there are no compositional fields, this
    # postprocessor will visualize the melt fraction of peridotite (calculated
    # using the anhydrous model of Katz, 2003). If there is at least one
    # compositional field, the postprocessor assumes that the  first
    # compositional field is the content of pyroxenite, and will visualize the
    # melt fraction for a mixture of peridotite and pyroxenite (using the
    # melting model of Sobolev, 2011 for pyroxenite). All the parameters that
    # were used in these calculations can be changed in the input file, the
    # most relevant maybe being the mass fraction of Cpx in peridotite in the
    # Katz melting model (Mass fraction cpx), which right now has a default of
    # 15\%. The corresponding p-T-diagrams can be generated by running the
    # tests melt\_postprocessor\_peridotite and
    # melt\_postprocessor\_pyroxenite.
    # 
    # `melt material properties': A visualization output object that generates
    # output for melt related properties of the material model. Note that this
    # postprocessor always outputs the compaction pressure, but can output a
    # large range of additional properties, as selected in the ``List of
    # properties'' parameter.
    # 
    # `named additional outputs': Some material models can compute quantities
    # other than those that typically appear in the equations that \aspect{}
    # solves (such as the viscosity, density, etc). Examples of quantities
    # material models may be able to compute are seismic velocities, or other
    # quantities that can be derived from the state variables and the material
    # coefficients such as the stress or stress anisotropies. These quantities
    # are generically referred to as `named outputs' because they are given an
    # explicit name different from the usual outputs of material models.
    # 
    # This visualization postprocessor outputs whatever quantities the
    # material model can compute. What quantities these are is specific to the
    # material model in use for a simulation, and for many models in fact does
    # not contain any named outputs at all.
    # 
    # `nonadiabatic pressure': A visualization output object that generates
    # output for the non-adiabatic component of the pressure.
    # 
    # The variable that is outputted this way is computed by taking the
    # pressure at each point and subtracting from it the adiabatic pressure
    # computed at the beginning of the simulation. Because the adiabatic
    # pressure is one way of defining a static pressure background field, what
    # this visualization postprocessor therefore produces is \textit{one} way
    # to compute a \textit{dynamic pressure}. There are, however, other ways
    # as well, depending on the choice of the ``background pressure''.
    # 
    # `nonadiabatic temperature': A visualization output object that generates
    # output for the non-adiabatic component of the temperature.
    # 
    # `particle count': A visualization output object that generates output
    # about the number of particles per cell.
    # 
    # `partition': A visualization output object that generates output for the
    # parallel partition that every cell of the mesh is associated with.
    # 
    # `principal stress': A visualization output object that outputs the
    # principal stress values and directions, i.e., the eigenvalues and
    # eigenvectors of the stress tensor. The postprocessor can either operate
    # on the full stress tensor or only on the deviatoric stress tensor.
    # 
    # `shear stress': A visualization output object that generates output for
    # the 3 (in 2d) or 6 (in 3d) components of the shear stress tensor, i.e.,
    # for the components of the tensor $-2\eta\varepsilon(\mathbf u)$ in the
    # incompressible case and $-2\eta\left[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I\right]$ in the
    # compressible case. The shear stress differs from the full stress tensor
    # by the absence of the pressure. Note that the convention of positive
    # compressive stress is followed.
    # 
    # `spd factor': A visualization output object that generates output for
    # the spd factor. The spd factor is a factor which scales a part of the
    # Jacobian used for the Newton solver to make sure that the Jacobian
    # remains positive definite.
    # 
    # `spherical velocity components': A visualization output object that
    # outputs the polar coordinates components $v_r$ and $v_\phi$ of the
    # velocity field in 2D and the spherical coordinates components $v_r$,
    # $v_{\phi}$ and $v_{\theta}$ of the velocity field in 3D.
    # 
    # `strain rate': A visualization output object that generates output for
    # the norm of the strain rate, i.e., for the quantity
    # $\sqrt{\varepsilon(\mathbf u):\varepsilon(\mathbf u)}$ in the
    # incompressible case and $\sqrt{[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I]:[\varepsilon(\mathbf
    # u)-\tfrac 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I]}$ in the
    # compressible case.
    # 
    # `strain rate tensor': A visualization output object that generates
    # output for the 4 (in 2d) or 9 (in 3d) components of the strain rate
    # tensor, i.e., for the components of the tensor $\varepsilon(\mathbf u)$
    # in the incompressible case and $\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I$ in the compressible
    # case.
    # 
    # `stress': A visualization output object that generates output for the 3
    # (in 2d) or 6 (in 3d) components of the stress tensor, i.e., for the
    # components of the tensor $-2\eta\varepsilon(\mathbf u)+pI$ in the
    # incompressible case and $-2\eta\left[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I\right]+pI$ in the
    # compressible case. Note that the convention of positive compressive
    # stress is followed.
    # 
    # `surface dynamic topography': A visualization output object that
    # generates output for the dynamic topography at the top and bottom of the
    # model space. The approach to determine the dynamic topography requires
    # us to compute the stress tensor and evaluate the component of it in the
    # direction in which gravity acts. In other words, we compute
    # $\sigma_{rr}={\hat g}^T(2 \eta \varepsilon(\mathbf u)-\frac 13
    # (\textrm{div}\;\mathbf u)I)\hat g - p_d$ where $\hat g = \mathbf
    # g/\|\mathbf g\|$ is the direction of the gravity vector $\mathbf g$ and
    # $p_d=p-p_a$ is the dynamic pressure computed by subtracting the
    # adiabatic pressure $p_a$ from the total pressure $p$ computed as part of
    # the Stokes solve. From this, the dynamic topography is computed using
    # the formula $h=\frac{\sigma_{rr}}{(\mathbf g \cdot \mathbf n)  \rho}$
    # where $\rho$ is the density at the cell center. For the bottom surface
    # we chose the convection that positive values are up (out) and negative
    # values are in (down), analogous to the deformation of the upper surface.
    # Note that this implementation takes the direction of gravity into
    # account, which means that reversing the flow in backward advection
    # calculations will not reverse the instantaneous topography because the
    # reverse flow will be divided by the reverse surface gravity.
    # 
    # In contrast to the `dynamic topography' visualization postprocessor,
    # this plugin really only evaluates the dynamic topography at faces of
    # cells that are adjacent to `bottom' and `top' boundaries, and only
    # outputs information on the surface of the domain, rather than padding
    # the information with zeros in the interior of the domain.
    # 
    # `surface stress': A visualization output object that generates output on
    # the surface of the domain for the 3 (in 2d) or 6 (in 3d) components of
    # the stress tensor, i.e., for the components of the tensor
    # $-2\eta\varepsilon(\mathbf u)+pI$ in the incompressible case and
    # $-2\eta\left[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I\right]+pI$ in the
    # compressible case. Note that the convention of positive compressive
    # stress is followed.
    # 
    # `temperature anomaly': A visualization output postprocessor that outputs
    # the temperature minus the depth-average of the temperature.The average
    # temperature is calculated using the lateral averaging function from the
    # ``depth average'' postprocessor and interpolated linearly between the
    # layers specified through ``Number of depth slices''
    # 
    # `vertical heat flux': A visualization output object that generates
    # output for the heat flux in the vertical direction, which is the sum of
    # the advective and the conductive heat flux, with the sign convention of
    # positive flux upwards.
    # 
    # `volume of fluid values': A visualization output object that outputs the
    # volume fraction and optionally a level set field and the interface
    # normal vectors of volume of fluid fields.
    # 
    # `volumetric strain rate': A visualization output object that generates
    # output for the volumetric strain rate, i.e., for the quantity
    # $\nabla\cdot\mathbf u = \textrm{div}\; \mathbf u = \textrm{trace}\;
    # \varepsilon(\mathbf u)$. This should be zero (in some average sense) in
    # incompressible convection models, but can be non-zero in compressible
    # models and models with melt transport.
    set List of output variables            = volumetric strain rate # default: 

    # VTU file output supports grouping files from several CPUs into a given
    # number of files using MPI I/O when writing on a parallel filesystem.
    # Select 0 for no grouping. This will disable parallel file output and
    # instead write one file per processor. A value of 1 will generate one big
    # file containing the whole solution, while a larger value will create
    # that many files (at most as many as there are MPI ranks).
    set Number of grouped files             = 16

    # The file format to be used for graphical output. The list of possible
    # output formats that can be given here is documented in the appendix of
    # the manual where the current parameter is described.
    set Output format                       = hdf5                   # default: vtu

    # For computations with deforming meshes, ASPECT uses an
    # Arbitrary-Lagrangian-Eulerian formulation to handle deforming the
    # domain, so the mesh has its own velocity field.  This may be written as
    # an output field by setting this parameter to true.
    set Output mesh velocity                = false

    # If set to true, quantities related to stress and strain are computed in
    # each vertex. Otherwise, an average per cell is computed.
    set Point-wise stress and strain        = false

    # On large clusters it can be advantageous to first write the output to a
    # temporary file on a local file system and later move this file to a
    # network file system. If this variable is set to a non-empty string it
    # will be interpreted as a temporary storage location.
    set Temporary output location           = 

    # The time interval between each generation of graphical output files. A
    # value of zero indicates that output should be generated in each time
    # step. Units: years if the 'Use years in output instead of seconds'
    # parameter is set; seconds otherwise.
    set Time between graphical output       = 0                      # default: 1e8

    # The maximum number of time steps between each generation of graphical
    # output files.
    set Time steps between graphical output = 2147483647

    # deal.II offers the possibility to write vtu files with higher order
    # representations of the output data. This means each cell will correctly
    # show the higher order representation of the output data instead of the
    # linear interpolation between vertices that ParaView and Visit usually
    # show. Note that activating this option is safe and recommended, but
    # requires that (i) ``Output format'' is set to ``vtu'', (ii)
    # ``Interpolate output'' is set to true, (iii) you use a sufficiently new
    # version of Paraview or Visit to read the files (Paraview version 5.5 or
    # newer, and Visit version to be determined), and (iv) you use deal.II
    # version 9.1.0 or newer.
    # The effect of using this option can be seen in the following picture:
    # 
    # \begin{center}
    # \includegraphics[width=0.5\textwidth]{viz/parameters/higher-order-output}\end{center}The
    # top figure shows the plain output without interpolation or higher order
    # output. The middle figure shows output that was interpolated as
    # discussed for the ``Interpolate output'' option. The bottom panel shows
    # higher order output that achieves better accuracy than the interpolated
    # output at a lower memory cost.
    set Write higher order output           = false

    # File operations can potentially take a long time, blocking the progress
    # of the rest of the model run. Setting this variable to `true' moves this
    # process into a background thread, while the rest of the model
    # continues.
    set Write in background thread          = false


    subsection Artificial viscosity composition
      # The name of the compositional field whose output should be
      # visualized.
      set Name of compositional field = 
    end

    subsection Compositional fields as vectors
      # A list of sets of compositional fields which should be output as
      # vectors. Sets are separated from each other by semicolons and vector
      # components within each set are separated by commas (e.g. $vec1_x$,
      # $vec1_y$ ; $vec2_x$, $vec2_y$) where each name must be a defined named
      # compositional field. If only one name is given in a set, it is
      # interpreted as the first in a sequence of dim consecutive
      # compositional fields.
      set Names of fields  = 

      # Names of vectors as they will appear in the output.
      set Names of vectors = 
    end

    subsection Heat flux map
      # A boolean flag that controls whether to output the heat flux map as a
      # point wise value, or as a cell-wise averaged value. The point wise
      # output is more accurate, but it currently omits prescribed heat flux
      # values at boundaries and advective heat flux that is caused by
      # velocities non-tangential to boundaries. If you do not use these two
      # features it is recommended to switch this setting on to benefit from
      # the increased output resolution.
      set Output point wise heat flux = false
    end

    subsection Material properties
      # A comma separated list of material properties that should be written
      # whenever writing graphical output. By default, the material properties
      # will always contain the density, thermal expansivity, specific heat
      # and viscosity. The following material properties are available:
      # 
      # viscosity|density|thermal expansivity|specific heat|thermal
      # conductivity|thermal diffusivity|compressibility|entropy derivative
      # temperature|entropy derivative pressure|reaction terms|melt fraction
      set List of material properties = density,thermal expansivity,specific heat,viscosity
    end

    subsection Melt fraction
      # Constant parameter in the quadratic function that approximates the
      # solidus of peridotite. Units: \si{\degreeCelsius}.
      set A1                = 1085.7

      # Prefactor of the linear pressure term in the quadratic function that
      # approximates the solidus of peridotite.
      # \si{\degreeCelsius\per\pascal}.
      set A2                = 1.329e-7

      # Prefactor of the quadratic pressure term in the quadratic function
      # that approximates the solidus of peridotite.
      # \si{\degreeCelsius\per\pascal\squared}.
      set A3                = -5.1e-18

      # Constant parameter in the quadratic function that approximates the
      # lherzolite liquidus used for calculating the fraction of
      # peridotite-derived melt. Units: \si{\degreeCelsius}.
      set B1                = 1475.0

      # Prefactor of the linear pressure term in the quadratic function that
      # approximates the  lherzolite liquidus used for calculating the
      # fraction of peridotite-derived melt. \si{\degreeCelsius\per\pascal}.
      set B2                = 8.0e-8

      # Prefactor of the quadratic pressure term in the quadratic function
      # that approximates the  lherzolite liquidus used for calculating the
      # fraction of peridotite-derived melt.
      # \si{\degreeCelsius\per\pascal\squared}.
      set B3                = -3.2e-18

      # Constant parameter in the quadratic function that approximates the
      # liquidus of peridotite. Units: \si{\degreeCelsius}.
      set C1                = 1780.0

      # Prefactor of the linear pressure term in the quadratic function that
      # approximates the liquidus of peridotite.
      # \si{\degreeCelsius\per\pascal}.
      set C2                = 4.50e-8

      # Prefactor of the quadratic pressure term in the quadratic function
      # that approximates the liquidus of peridotite.
      # \si{\degreeCelsius\per\pascal\squared}.
      set C3                = -2.0e-18

      # Constant parameter in the quadratic function that approximates the
      # solidus of pyroxenite. Units: \si{\degreeCelsius}.
      set D1                = 976.0

      # Prefactor of the linear pressure term in the quadratic function that
      # approximates the solidus of pyroxenite. Note that this factor is
      # different from the value given in Sobolev, 2011, because they use the
      # potential temperature whereas we use the absolute temperature.
      # \si{\degreeCelsius\per\pascal}.
      set D2                = 1.329e-7

      # Prefactor of the quadratic pressure term in the quadratic function
      # that approximates the solidus of pyroxenite.
      # \si{\degreeCelsius\per\pascal\squared}.
      set D3                = -5.1e-18

      # Prefactor of the linear depletion term in the quadratic function that
      # approximates the melt fraction of pyroxenite.
      # \si{\degreeCelsius\per\pascal}.
      set E1                = 663.8

      # Prefactor of the quadratic depletion term in the quadratic function
      # that approximates the melt fraction of pyroxenite.
      # \si{\degreeCelsius\per\pascal\squared}.
      set E2                = -611.4

      # Mass fraction of clinopyroxene in the peridotite to be molten. Units:
      # non-dimensional.
      set Mass fraction cpx = 0.15

      # Exponent of the melting temperature in the melt fraction calculation.
      # Units: non-dimensional.
      set beta              = 1.5

      # Constant in the linear function that approximates the clinopyroxene
      # reaction coefficient. Units: non-dimensional.
      set r1                = 0.5

      # Prefactor of the linear pressure term in the linear function that
      # approximates the clinopyroxene reaction coefficient. Units:
      # \si{\per\pascal}.
      set r2                = 8e-11
    end

    subsection Melt material properties
      # A comma separated list of melt properties that should be written
      # whenever writing graphical output. The following material properties
      # are available:
      # 
      # compaction viscosity|fluid viscosity|permeability|fluid density|fluid
      # density gradient|is melt cell|darcy coefficient|darcy coefficient no
      # cutoff|compaction length
      set List of properties = compaction viscosity,permeability
    end

    subsection Principal stress
      # Whether to use the deviatoric stress tensor instead of the full stress
      # tensor to compute principal stress directions and values.
      set Use deviatoric stress = false
    end

    subsection Temperature anomaly
      # Number of depth slices used to define average temperature.
      set Number of depth slices              = 20

      # If true, use the specified boundary temperatures as average
      # temperatures at the surface. If false, extrapolate the temperature
      # gradient between the first and second cells to the surface. This
      # option will only work for models with a fixed surface temperature.
      set Use maximal temperature for bottom  = true

      # Whether to use the minimal specified boundary temperature as the
      # bottom boundary temperature. This option will only work for models
      # with a fixed bottom boundary temperature.
      set Use minimal temperature for surface = true
    end

    subsection Volume of Fluid
      # Include the internal data for the interface normal on the unit cells
      set Output interface normals                = false

      # Include fields defined such that the 0 contour is the fluid interface
      set Output interface reconstruction contour = false
    end

    subsection Vp anomaly
      # Scheme to compute the average velocity-depth profile. The reference
      # profile option evaluates the conditions along the reference adiabat
      # according to the material model. The lateral average option instead
      # calculates a lateral average from subdivision of the mesh. The lateral
      # average option may produce spurious results where there are sharp
      # velocity changes.
      set Average velocity scheme = reference profile

      # Number of depth slices used to define average seismic compressional
      # wave velocities from which anomalies are calculated. Units:
      # non-dimensional.
      set Number of depth slices  = 50
    end

    subsection Vs anomaly
      # Scheme to compute the average velocity-depth profile. The reference
      # profile option evaluates the conditions along the reference adiabat
      # according to the material model. The lateral average option instead
      # calculates a lateral average from subdivision of the mesh. The lateral
      # average option may produce spurious results where there are sharp
      # velocity changes.
      set Average velocity scheme = reference profile

      # Number of depth slices used to define average seismic shear wave
      # velocities from which anomalies are calculated. Units:
      # non-dimensional.
      set Number of depth slices  = 50
    end

  end

end


subsection Prescribed Stokes solution
  # Select one of the following models:
  # 
  # `ascii data': Implementation of a model in which the velocity is derived
  # from files containing data in ascii format. Note the required format of
  # the input data: The first lines may contain any number of comments if they
  # begin with `#', but one of these lines needs to contain the number of grid
  # points in each dimension as for example `# POINTS: 3 3'. The order of the
  # data columns has to be `x', `y', `v${}_x$' , `v${}_y$' in a 2d model and
  # `x', `y', `z', `v${}_x$' , `v${}_y$' , `v${}_z$' in a 3d model. Note that
  # the data in the input files need to be sorted in a specific order: the
  # first coordinate needs to ascend first, followed by the second and the
  # third at last in order to assign the correct data to the prescribed
  # coordinates. If you use a spherical model, then the data will still be
  # handled as Cartesian, however the assumed grid changes. `x' will be
  # replaced by the radial distance of the point to the bottom of the model,
  # `y' by the azimuth angle and `z' by the polar angle measured positive from
  # the north pole. The grid will be assumed to be a latitude-longitude grid.
  # Note that the order of spherical coordinates is `r', `phi', `theta' and
  # not `r', `theta', `phi', since this allows for dimension independent
  # expressions.
  # 
  # `circle': This value describes a vector field that rotates around the
  # z-axis with constant angular velocity (i.e., with a velocity that
  # increases with distance from the axis). The pressure is set to zero.
  # 
  # `function': This plugin allows to prescribe the Stokes solution for the
  # velocity and pressure field in terms of an explicit formula. The format of
  # these functions follows the syntax understood by the muparser library, see
  # Section~\ref{sec:muparser-format}.
  set Model name = unspecified


  subsection Ascii data model
    # The name of a directory that contains the model data. This path may
    # either be absolute (if starting with a `/') or relative to the current
    # directory. The path may also include the special text
    # `$ASPECT_SOURCE_DIR' which will be interpreted as the path in which the
    # ASPECT source files were located when ASPECT was compiled. This
    # interpretation allows, for example, to reference files located in the
    # `data/' subdirectory of ASPECT.
    set Data directory = $ASPECT_SOURCE_DIR/data/prescribed-stokes-solution/

    # The file name of the model data.
    set Data file name = box_2d.txt

    # Scalar factor, which is applied to the model data. You might want to use
    # this to scale the input to a reference model. Another way to use this
    # factor is to convert units of the input files. For instance, if you
    # provide velocities in cm/yr set this factor to 0.01.
    set Scale factor   = 1.
  end

  subsection Compaction pressure function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Fluid pressure function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Fluid velocity function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Pressure function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Velocity function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

end


subsection Prescribed fields
  # Whether to use the indicator function for x-velocity as the pressure
  # indicator function. This is useful for models where the velocities and
  # pressures are prescribed in the same regions.
  set Use x velocity indicator for pressure indicator = true # default: false


  subsection Pressure function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0.0   # default: 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Pressure indicator function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = pi=3.14159, H=6.0e5, W=6.6e5, eps=0.01       # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = if( x<=(H-y)+eps | (  y>=5.5e5-eps  ), 1, 0) # default: 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Velocity function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = H=6.0e5, v=0.035355339, eps=0.01, width=50000                                                                                                                                                                      # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = if( x<=(H-y)+eps, v, if(x<=(H-y)+width*sqrt(2), v*(0.5 * (1 + cos(pi*(x-(H-y))/(width*sqrt(2))))), 0.0)); if( x<=(H-y)+eps,-v, if(x<=(H-y)+width*sqrt(2),-v*(0.5 * (1 + cos(pi*(x-(H-y))/(width*sqrt(2))))), 0.0)) # default: 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

  subsection Velocity indicator function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = pi=3.14159, H=6.0e5, W=6.6e5, eps=0.01                                                     # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the muparser
    # library at http://muparser.beltoforion.de/.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = if( x<=(H-y)+eps | (  y>=5.5e5-eps  ), 1, 0); if( x<=(H-y)+eps | (  y>=5.5e5-eps  ), 1, 0) # default: 0; 0

    # The names of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

end


subsection Solver parameters
  # The relative tolerance up to which the linear system for the composition
  # system gets solved. See `Stokes solver parameters/Linear solver tolerance'
  # for more details.
  set Composition solver tolerance = 1e-12

  # The relative tolerance up to which the linear system for the temperature
  # system gets solved. See `Stokes solver parameters/Linear solver tolerance'
  # for more details.
  set Temperature solver tolerance = 1e-12


  subsection AMG parameters
    # This threshold tells the AMG setup how the coarsening should be
    # performed. In the AMG used by ML, all points that strongly couple with
    # the tentative coarse-level point form one aggregate. The term strong
    # coupling is controlled by the variable aggregation\_threshold, meaning
    # that all elements that are not smaller than aggregation\_threshold times
    # the diagonal element do couple strongly. The default is strongly
    # recommended. There are indications that for the Newton solver a
    # different value might be better. For extensive benchmarking of various
    # settings of the AMG parameters in this section for the Stokes problem
    # and others, see https://github.com/geodynamics/aspect/pull/234.
    set AMG aggregation threshold = 0.001

    # Turns on extra information on the AMG solver. Note that this will
    # generate much more output.
    set AMG output details        = false

    # Determines how many sweeps of the smoother should be performed. When the
    # flag elliptic is set to true, (which is true for ASPECT), the polynomial
    # degree of the Chebyshev smoother is set to this value. The term sweeps
    # refers to the number of matrix-vector products performed in the
    # Chebyshev case. In the non-elliptic case, this parameter sets the number
    # of SSOR relaxation sweeps for post-smoothing to be performed. The
    # default is strongly recommended. There are indications that for the
    # Newton solver a different value might be better. For extensive
    # benchmarking of various settings of the AMG parameters in this section
    # for the Stokes problem and others, see
    # https://github.com/geodynamics/aspect/pull/234.
    set AMG smoother sweeps       = 2

    # This parameter sets the type of smoother for the AMG. The default is
    # strongly recommended for any normal runs with ASPECT. There are some
    # indications that the symmetric Gauss-Seidel might be better and more
    # stable for the Newton solver. For extensive benchmarking of various
    # settings of the AMG parameters in this section for the Stokes problem
    # and others, see https://github.com/geodynamics/aspect/pull/234.
    set AMG smoother type         = Chebyshev
  end

  subsection Advection solver parameters
    # This is the number of iterations that define the GMRES solver restart
    # length. Increasing this parameter makes the solver more robust and
    # decreases the number of iterations. Be aware that increasing this number
    # increases the memory usage of the advection solver, and makes individual
    # iterations more expensive.
    set GMRES solver restart length = 50
  end

  subsection Diffusion solver parameters
    # Set a length scale for the diffusion of compositional fields if the
    # ``prescribed field with diffusion'' method is selected for a field. More
    # precisely, this length scale represents the square root of the product
    # of diffusivity and time in the diffusion equation, and controls the
    # distance over which features are diffused. Units: \si{\meter}.
    set Diffusion length scale = 1.e4
  end

  subsection Newton solver parameters
    # The maximum number of line search iterations allowed. If the criterion
    # is not reached after this number of iterations, we apply the scaled
    # increment even though it does not satisfy the necessary criteria and
    # simply continue with the next Newton iteration.
    set Max Newton line search iterations                 = 5

    # If the 'Nonlinear Newton solver switch tolerance' is reached before the
    # maximal number of Picard iterations, then the solver switches to Newton
    # solves anyway.
    set Max pre-Newton nonlinear iterations               = 10

    # The linear Stokes solver tolerance is dynamically chosen for the Newton
    # solver, based on the Eisenstat walker 1994 paper
    # (https://doi.org/10.1137/0917003), equation 2.2. Because this value can
    # become larger then one, we limit this value by this parameter.
    set Maximum linear Stokes solver tolerance            = 0.9

    # A relative tolerance with respect to the residual of the first
    # iteration, up to which the nonlinear Picard solver will iterate, before
    # changing to the Newton solver.
    set Nonlinear Newton solver switch tolerance          = 1e-5

    # When stabilizing the Newton matrix, we can encounter situations where
    # the coefficient inside the elliptic (top-left) block becomes negative or
    # zero. This coefficient has the form $1+x$ where $x$ can sometimes be
    # smaller than $-1$. In this case, the top-left block of the matrix is no
    # longer positive definite, and both preconditioners and iterative solvers
    # may fail. To prevent this, the stabilization computes an $\alpha$ so
    # that $1+\alpha x$ is never negative. This $\alpha$ is chosen as $1$ if
    # $x\ge -1$, and $\alpha=-\frac 1x$ otherwise. (Note that this always
    # leads to $0\le \alpha \le 1$.)  On the other hand, we also want to stay
    # away from $1+\alpha x=0$, and so modify the choice of $\alpha$ to be $1$
    # if $x\ge -c$, and $\alpha=-\frac cx$ with a $c$ between zero and one.
    # This way, if $c<1$, we are assured that $1-\alpha x>c$, i.e., bounded
    # away from zero.
    set SPD safety factor                                 = 0.9

    # This parameters allows for the stabilization of the preconditioner. If
    # one derives the Newton method without any modifications, the matrix
    # created for the preconditioning is not necessarily Symmetric Positive
    # Definite. This is problematic (see \cite{FBTGS19}). When `none' is
    # chosen, the preconditioner is not stabilized. The `symmetric' parameters
    # symmetrizes the matrix, and `PD' makes the matrix Positive Definite.
    # `SPD' is the full stabilization, where the matrix is guaranteed
    # Symmetric Positive Definite.
    set Stabilization preconditioner                      = SPD

    # This parameters allows for the stabilization of the velocity block. If
    # one derives the Newton method without any modifications, the matrix
    # created for the velocity block is not necessarily Symmetric Positive
    # Definite. This is problematic (see \cite{FBTGS19}). When `none' is
    # chosen, the velocity block is not stabilized. The `symmetric' parameters
    # symmetrizes the matrix, and `PD' makes the matrix Positive Definite.
    # `SPD' is the full stabilization, where the matrix is guaranteed
    # Symmetric Positive Definite.
    set Stabilization velocity block                      = SPD

    # If set to true, the Picard iteration uses the Eisenstat Walker method to
    # determine how accurately linear systems need to be solved. The Picard
    # iteration is used, for example, in the first few iterations of the
    # Newton method before the matrix is built including derivatives of the
    # model, since the Picard iteration generally converges even from points
    # where Newton's method does not.
    # 
    # Once derivatives are used in a Newton method, \aspect{} always uses the
    # Eisenstat Walker method.
    set Use Eisenstat Walker method for Picard iterations = false

    # When this parameter is true and the linear solver fails, we try again,
    # but now with SPD stabilization for both the preconditioner and the
    # velocity block. The SPD stabilization will remain active until the next
    # timestep, when the default values are restored.
    set Use Newton failsafe                               = false

    # This method allows to slowly introduce the derivatives based on the
    # improvement of the residual. If set to false, the scaling factor for the
    # Newton derivatives is set to one immediately when switching on the
    # Newton solver. When this is set to true, the derivatives are slowly
    # introduced by the following equation: $\max(0.0,
    # (1.0-(residual/switch\_initial\_residual)))$, where
    # switch\_initial\_residual is the residual at the time when the Newton
    # solver is switched on.
    set Use Newton residual scaling method                = false
  end

  subsection Operator splitting parameters
    # Set a time step size for computing reactions of compositional fields and
    # the temperature field in case operator splitting is used. This is only
    # used when the parameter ``Use operator splitting'' is set to true. The
    # reaction time step must be greater than 0. If you want to prescribe the
    # reaction time step only as a relative value compared to the advection
    # time step as opposed to as an absolute value, you should use the
    # parameter ``Reaction time steps per advection step'' and set this
    # parameter to the same (or larger) value as the ``Maximum time step''
    # (which is 5.69e+300 by default). Units: Years or seconds, depending on
    # the ``Use years in output instead of seconds'' parameter.
    set Reaction time step                     = 1000.0

    # The number of reaction time steps done within one advection time step in
    # case operator splitting is used. This is only used if the parameter
    # ``Use operator splitting'' is set to true. If set to zero, this
    # parameter is ignored. Otherwise, the reaction time step size is chosen
    # according to this criterion and the ``Reaction time step'', whichever
    # yields the smaller time step. Units: none.
    set Reaction time steps per advection step = 0
  end

  subsection Stokes solver parameters
    # This is the number of iterations that define the GMRES solver restart
    # length. Increasing this parameter helps with convergence issues arising
    # from high localized viscosity jumps in the domain. Be aware that
    # increasing this number increases the memory usage of the Stokes solver,
    # and makes individual Stokes iterations more expensive.
    set GMRES solver restart length                     = 50

    # This is the sole parameter for the IDR(s) Krylov solver and will dictate
    # the number of matrix-vector products and preconditioner applications per
    # iteration (s+1) and the total number of temporary vectors required
    # (5+3*s). For s=1, this method is analogous to BiCGStab. As s is
    # increased this method is expected to converge to GMRES in terms of
    # matrix-vector/preconditioner applications to solution.
    set IDR(s) parameter                                = 2

    # This is the Krylov method used to solve the Stokes system. Both options,
    # GMRES and IDR(s), solve non-symmetric, indefinite systems. GMRES
    # guarantees the residual will be reduced in each iteration while IDR(s)
    # has no such property. On the other hand, the vector storage requirement
    # for GMRES is dependent on the restart length and can be quite
    # restrictive (since, for the matrix-free GMG solver, memory is dominated
    # by these vectors) whereas IDR(s) has a short term recurrence. Note that
    # the IDR(s) Krylov method is not available for the AMG solver since it is
    # not a flexible method, i.e., it cannot handle a preconditioner which may
    # change in each iteration (the AMG-based preconditioner contains a CG
    # solve in the pressure space which may have different number of
    # iterations each step).
    set Krylov method for cheap solver steps            = GMRES

    # A relative tolerance up to which the approximate inverse of the $A$
    # block of the Stokes system is computed. This approximate $A$ is used in
    # the preconditioning used in the GMRES solver. The exact definition of
    # this block preconditioner for the Stokes equation can be found in
    # \cite{KHB12}.
    set Linear solver A block tolerance                 = 1e-2

    # A relative tolerance up to which the approximate inverse of the $S$
    # block (i.e., the Schur complement matrix $S = BA^{-1}B^{T}$) of the
    # Stokes system is computed. This approximate inverse of the $S$ block is
    # used in the preconditioning used in the GMRES solver. The exact
    # definition of this block preconditioner for the Stokes equation can be
    # found in \cite{KHB12}.
    set Linear solver S block tolerance                 = 1e-6

    # A relative tolerance up to which the linear Stokes systems in each time
    # or nonlinear step should be solved. The absolute tolerance will then be
    # $\| M x_0 - F \| \cdot \text{tol}$, where $x_0 = (0,p_0)$ is the initial
    # guess of the pressure, $M$ is the system matrix, $F$ is the right-hand
    # side, and tol is the parameter specified here. We include the initial
    # guess of the pressure to remove the dependency of the tolerance on the
    # static pressure. A given tolerance value of 1 would mean that a zero
    # solution vector is an acceptable solution since in that case the norm of
    # the residual of the linear system equals the norm of the right hand
    # side. A given tolerance of 0 would mean that the linear system has to be
    # solved exactly, since this is the only way to obtain a zero residual.
    # 
    # In practice, you should choose the value of this parameter to be so that
    # if you make it smaller the results of your simulation do not change any
    # more (qualitatively) whereas if you make it larger, they do. For most
    # cases, the default value should be sufficient. In fact, a tolerance of
    # 1e-4 might be accurate enough.
    set Linear solver tolerance                         = 1.0e-7    # default: 1e-7

    # This sets the maximum number of iterations used in the expensive Stokes
    # solver. If this value is set too low for the size of the problem, the
    # Stokes solver will not converge and return an error message pointing out
    # that the user didn't allow a sufficiently large number of iterations for
    # the iterative solver to converge.
    set Maximum number of expensive Stokes solver steps = 10000     # default: 1000

    # As explained in the paper that describes ASPECT (Kronbichler, Heister,
    # and Bangerth, 2012, see \cite{KHB12}) we first try to solve the Stokes
    # system in every time step using a GMRES iteration with a poor but cheap
    # preconditioner. By default, we try whether we can converge the GMRES
    # solver in 200 such iterations before deciding that we need a better
    # preconditioner. This is sufficient for simple problems with variable
    # viscosity and we never need the second phase with the more expensive
    # preconditioner. On the other hand, for more complex problems, and in
    # particular for problems with strongly nonlinear viscosity, the 200 cheap
    # iterations don't actually do very much good and one might skip this part
    # right away. In that case, this parameter can be set to zero, i.e., we
    # immediately start with the better but more expensive preconditioner.
    set Number of cheap Stokes solver steps             = 200

    # This is the type of solver used on the Stokes system. The block
    # geometric multigrid solver currently has a limited implementation and
    # therefore may trigger Asserts in the code when used. If this is the
    # case, please switch to 'block AMG'. Additionally, the block GMG solver
    # requires using material model averaging.
    set Stokes solver type                              = block AMG

    # If set to true the linear system for the Stokes equation will be solved
    # using Trilinos klu, otherwise an iterative Schur complement solver is
    # used. The direct solver is only efficient for small problems.
    set Use direct solver for Stokes system             = false

    # This parameter determines whether we use an simplified approximation of
    # the $A$ block as preconditioner for the Stokes solver, or the full $A$
    # block. The simplified approximation only contains the terms that
    # describe the coupling of identical components (plus boundary conditions)
    # as described in \cite{KHB12}. The full block is closer to the
    # description in \cite{rudi2017weighted}.
    # 
    # There is no clear way to determine which preconditioner performs better.
    # The default value (simplified approximation) requires more outer GMRES
    # iterations, but is faster to apply in each iteration. The full block
    # needs less assembly time (because the block is available anyway),
    # converges in less GMRES iterations, but requires more time per
    # iteration. There are also differences in the amount of memory
    # consumption between the two approaches.
    # 
    # The default value should be good for relatively simple models, but in
    # particular for very strong viscosity contrasts the full $A$ block can be
    # advantageous.
    set Use full A block as preconditioner              = false
  end

end


subsection Temperature field
  # A comma separated list denoting the solution method of the temperature
  # field. Each entry of the list must be one of the currently implemented
  # field types.
  # 
  # These choices correspond to the following methods by which the temperature
  # field gains its values:\begin{itemize}\item ``field'': If the temperature
  # is marked with this method, then its values are computed in each time step
  # by solving the temperature advection-diffusion equation. In other words,
  # this corresponds to the usual notion of a temperature.
  # \item ``prescribed field'': The value of the temperature is determined in
  # each time step from the material model. If a compositional field is marked
  # with this method, then the value of a specific additional material model
  # output, called the `PrescribedTemperatureOutputs' is interpolated onto the
  # temperature. This field does not change otherwise, it is not advected with
  # the flow.
  # \end{itemize}
  set Temperature method = field
end


subsection Termination criteria
  # Whether to checkpoint the simulation right before termination.
  set Checkpoint on termination = true     # default: false

  # Terminate the simulation once the specified timestep has been reached.
  set End step                  = 1        # default: 100

  # A comma separated list of termination criteria that will determine when
  # the simulation should end. Whether explicitly stated or not, the ``end
  # time'' termination criterion will always be used.The following termination
  # criteria are available:
  # 
  # `end step': Terminate the simulation once the specified timestep has been
  # reached.
  # 
  # `end time': Terminate the simulation once the end time specified in the
  # input file has been reached. Unlike all other termination criteria, this
  # criterion is \textit{always} active, whether it has been explicitly
  # selected or not in the input file (this is done to preserve historical
  # behavior of \aspect{}, but it also likely does not inconvenience anyone
  # since it is what would be selected in most cases anyway).
  # 
  # `steady state temperature': A criterion that terminates the simulation
  # when the global integral of the temperature field stays within a certain
  # range for a specified period of time.
  # 
  # `steady state velocity': A criterion that terminates the simulation when
  # the RMS of the velocity field stays within a certain range for a specified
  # period of time.
  # 
  # `user request': Terminate the simulation gracefully when a file with a
  # specified name appears in the output directory. This allows the user to
  # gracefully exit the simulation at any time by simply creating such a file
  # using, for example, \texttt{touch output/terminate}. The file's location
  # is chosen to be in the output directory, rather than in a generic location
  # such as the ASPECT directory, so that one can run multiple simulations at
  # the same time (which presumably write to different output directories) and
  # can selectively terminate a particular one.
  # 
  # `wall time': Terminate the simulation once the wall time limit has
  # reached.
  set Termination criteria      = end time

  # The wall time of the simulation. Unit: hours.
  set Wall time                 = 24.


  subsection Steady state temperature
    # The maximum relative deviation of the temperature in recent simulation
    # time for the system to be considered in steady state. If the actual
    # deviation is smaller than this number, then the simulation will be
    # terminated.
    set Maximum relative deviation = 0.05

    # The minimum length of simulation time that the system should be in
    # steady state before termination.Units: years if the 'Use years in output
    # instead of seconds' parameter is set; seconds otherwise.
    set Time in steady state       = 1e7
  end

  subsection Steady state velocity
    # The maximum relative deviation of the RMS in recent simulation time for
    # the system to be considered in steady state. If the actual deviation is
    # smaller than this number, then the simulation will be terminated.
    set Maximum relative deviation = 0.05

    # The minimum length of simulation time that the system should be in
    # steady state before termination.Units: years if the 'Use years in output
    # instead of seconds' parameter is set; seconds otherwise.
    set Time in steady state       = 1e7
  end

  subsection User request
    # The name of a file that, if it exists in the output directory (whose
    # name is also specified in the input file) will lead to termination of
    # the simulation. The file's location is chosen to be in the output
    # directory, rather than in a generic location such as the ASPECT
    # directory, so that one can run multiple simulations at the same time
    # (which presumably write to different output directories) and can
    # selectively terminate a particular one.
    set File name = terminate-aspect
  end

end


subsection Time stepping
  # A comma separated list of time stepping plugins that will be used to
  # calculate the time step size. The minimum of the  result of each plugin
  # will be used.
  # 
  # The following plugins are available:
  # 
  # `conduction time step': This model computes the conduction time step as
  # the minimum over all cells of $ CFL h^2 \cdot \rho C_p / k$, where k is
  # the thermal conductivity. This plugin will always request advancing to the
  # next time step.
  # 
  # `convection time step': This model computes the convection time step as $
  # CFL / \max \| u \| / h$ over all cells, where $u$ is the velocity and $h$
  # is the product of mesh size and temperature polynomial degree.
  # 
  # `function': This model uses a time step specified in the parameter file
  # specified as a function of time. This plugin will always request advancing
  # to the next time step.
  # 
  # `repeat on cutback': This time stepping plugin will detect a situation
  # where the computed time step shrinks by more than a user-controlled
  # factor. In that situation, the previous time step will be repeated with a
  # smaller step size.
  # A large reduction in time step size typically happens when velocities
  # change abruptly. Repeating the time step ensure properly resolving this
  # event. It is useful to consider setting the "Maximum relative increase in
  # time step" option to avoid repeatedly repeating every other time step.
  set List of model names    = 

  # Specifiy a minimum time step size (or 0 to disable).
  set Minimum time step size = 0.


  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # Expression for the time step size as a function of 'time'.
    set Function expression = 1.0

    # Name for the variable representing the current time.
    set Variable names      = time
  end

  subsection Repeat on cutback
    # A factor that controls the size of the time step when repeating. The
    # default of 0.5 corresponds to 50\% of the original step taken.
    set Cut back amount           = 0.5

    # A factor that controls when a step is going to be repeated. If the newly
    # computed step size is smaller than the last step size multiplied by this
    # factor, the step is repeated.
    set Relative repeat threshold = 0.2
  end

end


subsection Volume of Fluid
  # Number of divisions per dimension when computing the initial volume
  # fractions.If set to the default of 3 for a 2D model, then initialization
  # will be based on the initialization criterion at $3^2=9$ points within
  # each cell. If the initialization based on a composition style initial
  # condition, a larger value may be desired for better approximation of the
  # initial fluid fractions. Smaller values will suffice in the case of level
  # set initializations due to the presence of more information to better
  # approximate the initial fluid fractions.
  set Number initialization samples    = 3

  # Minimum significant volume. Fluid fractions below this value are
  # considered to be zero.
  set Volume fraction threshold        = 1e-6

  # The relative tolerance up to which the linear system for the Volume of
  # Fluid system gets solved. See 'Solver parameters/Composition solver
  # tolerance' for more details.
  set Volume of Fluid solver tolerance = 1e-12
end