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FEniCS GitHub Actions committed Nov 15, 2024
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4 changes: 2 additions & 2 deletions dolfinx/main/cpp/demos/demo_biharmonic.html
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Expand Up @@ -136,8 +136,8 @@ <h3>Weak formulation<a class="headerlink" href="#weak-formulation" title="Link t
\forall \ K \in \mathcal{T} \right\}
\]</div>
<p>and considering the boundary conditions</p>
<div class="amsmath math notranslate nohighlight" id="equation-1125d635-100a-4f86-a578-cda74b7276d4">
<span class="eqno">(1)<a class="headerlink" href="#equation-1125d635-100a-4f86-a578-cda74b7276d4" title="Permalink to this equation"></a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-d7cb6ec5-e6c7-4b98-9d50-f08c488ff825">
<span class="eqno">(1)<a class="headerlink" href="#equation-d7cb6ec5-e6c7-4b98-9d50-f08c488ff825" title="Permalink to this equation"></a></span>\[\begin{align}
u &amp;= 0 \quad {\rm on} \ \partial\Omega, \\
\nabla^{2} u &amp;= 0 \quad {\rm on} \ \partial\Omega,
\end{align}\]</div>
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"cells": [
{
"cell_type": "markdown",
"id": "3191ec18",
"id": "d3a49a9b",
"metadata": {},
"source": [
"# Matrix-free conjugate gradient solver for the Poisson equation\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "84bc3408",
"id": "8bfdff63",
"metadata": {},
"outputs": [],
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{
"cell_type": "code",
"execution_count": null,
"id": "07b0d6bc",
"id": "084bc6d6",
"metadata": {},
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"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "73beaab9",
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"metadata": {},
"outputs": [],
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},
{
"cell_type": "markdown",
"id": "8e23f975",
"id": "72486968",
"metadata": {},
"source": [
"We begin by using {py:func}`create_rectangle\n",
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{
"cell_type": "code",
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"id": "dd8845f5",
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"metadata": {},
"outputs": [],
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{
"cell_type": "code",
"execution_count": null,
"id": "8ec91826",
"id": "b60a2fe5",
"metadata": {},
"outputs": [],
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},
{
"cell_type": "markdown",
"id": "f8befbac",
"id": "58bd4345",
"metadata": {},
"source": [
"The second argument to {py:class}`functionspace\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "e1681538",
"id": "c9711735",
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},
{
"cell_type": "markdown",
"id": "9ab4f97a",
"id": "be539179",
"metadata": {},
"source": [
"We now find the degrees of freedom that are associated with the boundary\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "828cfecc",
"id": "c46cd099",
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},
{
"cell_type": "markdown",
"id": "1b3f6ce4",
"id": "833014b2",
"metadata": {},
"source": [
"and use {py:func}`dirichletbc <dolfinx.fem.dirichletbc>` to define the\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "93131540",
"id": "ed378695",
"metadata": {},
"outputs": [],
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},
{
"cell_type": "markdown",
"id": "01aa6d42",
"id": "b81f2662",
"metadata": {},
"source": [
"Next, we express the variational problem using UFL."
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{
"cell_type": "code",
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"id": "d7828bad",
"id": "c7f34588",
"metadata": {},
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},
{
"cell_type": "markdown",
"id": "8289288b",
"id": "b2104a6e",
"metadata": {},
"source": [
"For the matrix-free solvers we also define a second linear form `M` as\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "403cce4c",
"id": "a61d6a7b",
"metadata": {},
"outputs": [],
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},
{
"cell_type": "markdown",
"id": "307b3fe4",
"id": "f27a0949",
"metadata": {},
"source": [
"### Matrix-free conjugate gradient solver\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "960a881e",
"id": "815055f7",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "cd6b2778",
"id": "19d8fb7e",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "5eb8f258",
"id": "40cdb523",
"metadata": {
"lines_to_next_cell": 2
},
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{
"cell_type": "code",
"execution_count": null,
"id": "a723f41a",
"id": "da5be6c5",
"metadata": {
"lines_to_next_cell": 2
},
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},
{
"cell_type": "markdown",
"id": "4064d31c",
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"metadata": {
"lines_to_next_cell": 2
},
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{
"cell_type": "code",
"execution_count": null,
"id": "f7147d82",
"id": "b9269c01",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "8bf5c788",
"id": "047ea087",
"metadata": {},
"source": [
"This matrix-free solver is now used to compute the finite element solution.\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "e68ea075",
"id": "5fd3ea85",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "c5756c39",
"id": "f091ed71",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "65b13ba3",
"id": "1bfcdccc",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "8e63ae28",
"id": "995dce2d",
"metadata": {},
"outputs": [],
"source": [
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"cells": [
{
"cell_type": "markdown",
"id": "2b4055aa",
"id": "bb323bc9",
"metadata": {},
"source": [
"# Mixed formulation for the Poisson equation"
]
},
{
"cell_type": "markdown",
"id": "73a2ae48",
"id": "c331a722",
"metadata": {},
"source": [
"This demo illustrates how to solve Poisson equation using a mixed\n",
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},
{
"cell_type": "markdown",
"id": "fa02d3f9",
"id": "564e5647",
"metadata": {},
"source": [
"```{admonition} Download sources\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "eca194ef",
"id": "c1cecfd6",
"metadata": {},
"outputs": [],
"source": [
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2 changes: 1 addition & 1 deletion dolfinx/main/python/_modules/dolfinx/io/gmshio.html
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Expand Up @@ -322,7 +322,7 @@ <h1>Source code for dolfinx.io.gmshio</h1><div class="highlight"><pre>
<span class="sd"> Note:</span>
<span class="sd"> For performance, this function should only be called once for</span>
<span class="sd"> large problems. For re-use, it is recommended to save the mesh</span>
<span class="sd"> and corresponding tags using :class:`dolfinxio.XDMFFile` after</span>
<span class="sd"> and corresponding tags using :class:`dolfinx.io.XDMFFile` after</span>
<span class="sd"> creation for efficient access.</span>

<span class="sd"> &quot;&quot;&quot;</span>
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2 changes: 1 addition & 1 deletion dolfinx/main/python/generated/dolfinx.io.gmshio.html
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<p class="admonition-title">Note</p>
<p>For performance, this function should only be called once for
large problems. For re-use, it is recommended to save the mesh
and corresponding tags using <code class="xref py py-class docutils literal notranslate"><span class="pre">dolfinxio.XDMFFile</span></code> after
and corresponding tags using <a class="reference internal" href="dolfinx.io.html#dolfinx.io.XDMFFile" title="dolfinx.io.XDMFFile"><code class="xref py py-class docutils literal notranslate"><span class="pre">dolfinx.io.XDMFFile</span></code></a> after
creation for efficient access.</p>
</div>
</dd></dl>
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2 changes: 1 addition & 1 deletion dolfinx/main/python/searchindex.js

Large diffs are not rendered by default.

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