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‎dolfinx/main/cpp/demos/demo_biharmonic.html

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\forall \ K \in \mathcal{T} \right\}
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\]</div>
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<p>and considering the boundary conditions</p>
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<div class="amsmath math notranslate nohighlight" id="equation-79c699de-77cf-4844-9553-75a79d1abdd0">
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<span class="eqno">(1)<a class="headerlink" href="#equation-79c699de-77cf-4844-9553-75a79d1abdd0" title="Permalink to this equation"></a></span>\[\begin{align}
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<div class="amsmath math notranslate nohighlight" id="equation-62e78a09-e811-4d83-bde0-ced93b0af10f">
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<span class="eqno">(1)<a class="headerlink" href="#equation-62e78a09-e811-4d83-bde0-ced93b0af10f" title="Permalink to this equation"></a></span>\[\begin{align}
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u &amp;= 0 \quad {\rm on} \ \partial\Omega, \\
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\nabla^{2} u &amp;= 0 \quad {\rm on} \ \partial\Omega,
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\end{align}\]</div>

‎dolfinx/main/python/_downloads/9561cf6cd1a70079b986f4eb31580cbd/demo_poisson_matrix_free.ipynb

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"cells": [
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"cell_type": "markdown",
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"# Matrix-free conjugate gradient solver for the Poisson equation\n",
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{
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{
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"We begin by using {py:func}`create_rectangle\n",
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{
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"cell_type": "code",
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"The second argument to {py:class}`functionspace\n",
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{
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},
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"We now find the degrees of freedom that are associated with the boundary\n",
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{
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"and use {py:func}`dirichletbc <dolfinx.fem.dirichletbc>` to define the\n",
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"Next, we express the variational problem using UFL."
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"For the matrix-free solvers we also define a second linear form `M` as\n",
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"### Matrix-free conjugate gradient solver\n",
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"This matrix-free solver is now used to compute the finite element\n",
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