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+      <li class="breadcrumb-item active">fastvpinns.FE.basis_function_2d</li>
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+
+  <h1>Source code for fastvpinns.FE.basis_function_2d</h1><div class="highlight"><pre>
+<span></span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">The file `basis_function_2d.py` contains a wrapper class for all the finite element basis functions </span>
+<span class="sd">used in the FE2D code. The 2D basis functions have methods to return the value </span>
+<span class="sd">of the basis function and its derivatives at the reference point (xi, eta).</span>
+
+<span class="sd">Author: Thivin Anandh D</span>
+
+<span class="sd">Changelog: 30/Aug/2023 - First version</span>
+
+<span class="sd">Known issues: None</span>
+
+<span class="sd">Dependencies: None specified</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">abstractmethod</span>
+
+
+<div class="viewcode-block" id="BasisFunction2D">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D">[docs]</a>
+<span class="k">class</span> <span class="nc">BasisFunction2D</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    This class defines the basis functions for a 2D element.</span>
+
+<span class="sd">    :num_shape_functions (int): The number of shape functions.</span>
+<span class="sd">    :value(xi, eta): Evaluates the basis function at the given xi and eta coordinates.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num_shape_functions</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">num_shape_functions</span> <span class="o">=</span> <span class="n">num_shape_functions</span>
+
+<div class="viewcode-block" id="BasisFunction2D.value">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.value">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">value</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Evaluates the basis function at the given xi and eta coordinates.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The value of the basis function at the given coordinates.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="BasisFunction2D.gradx">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.gradx">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">gradx</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Computes the partial derivative of the basis function with respect to xi.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The partial derivative of the basis function with respect to xi.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="BasisFunction2D.grady">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.grady">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">grady</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Computes the partial derivative of the basis function with respect to eta.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The partial derivative of the basis function with respect to eta.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="BasisFunction2D.gradxx">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.gradxx">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">gradxx</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Computes the second partial derivative of the basis function with respect to xi.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The second partial derivative of the basis function with respect to xi.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="BasisFunction2D.gradxy">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.gradxy">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">gradxy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Computes the mixed partial derivative of the basis function with respect to xi and eta.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The mixed partial derivative of the basis function with respect to xi and eta.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="BasisFunction2D.gradyy">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_basis_function.html#fastvpinns.FE.basis_function_2d.BasisFunction2D.gradyy">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">gradyy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Computes the second partial derivative of the basis function with respect to eta.</span>
+
+<span class="sd">        :param float xi: The xi coordinate.</span>
+<span class="sd">        :param float eta: The eta coordinate.</span>
+<span class="sd">        :return: The second partial derivative of the basis function with respect to eta.</span>
+<span class="sd">        :rtype: float</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">pass</span></div>
+</div>
+
+
+
+<span class="c1"># ---------------- Legendre -------------------------- #</span>
+<span class="kn">from</span> <span class="nn">.basis_2d_QN_Legendre</span> <span class="kn">import</span> <span class="o">*</span>  <span class="c1"># Normal Legendre from Jacobi -&gt; J(n) = J(n-1) - J(n+1)</span>
+<span class="kn">from</span> <span class="nn">.basis_2d_QN_Legendre_Special</span> <span class="kn">import</span> <span class="o">*</span>  <span class="c1"># L(n) = L(n-1) - L(n+1)</span>
+
+<span class="c1"># ---------------- Jacobi -------------------------- #</span>
+<span class="kn">from</span> <span class="nn">.basis_2d_QN_Jacobi</span> <span class="kn">import</span> <span class="o">*</span>  <span class="c1"># Normal Jacobi</span>
+
+<span class="c1"># ---------------- Chebyshev -------------------------- #</span>
+<span class="kn">from</span> <span class="nn">.basis_2d_QN_Chebyshev_2</span> <span class="kn">import</span> <span class="o">*</span>  <span class="c1"># Normal Chebyshev</span>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
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+    <p>&#169; Copyright 2024, Thivin Anandh, Divij Ghose, Sashikumaar Ganesan.</p>
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