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FEniCS GitHub Actions committed Nov 17, 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-d7dde6db-390d-4be7-a5ef-8b27c5dd58c8">
<span class="eqno">(1)<a class="headerlink" href="#equation-d7dde6db-390d-4be7-a5ef-8b27c5dd58c8" title="Permalink to this equation"></a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-23089306-fc60-4001-ae92-274c2fe7b4d2">
<span class="eqno">(1)<a class="headerlink" href="#equation-23089306-fc60-4001-ae92-274c2fe7b4d2" 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": "e1a24d08",
"id": "65abf16a",
"metadata": {},
"source": [
"# Matrix-free conjugate gradient solver for the Poisson equation\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "950f74b1",
"id": "4589adf4",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -82,7 +82,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "d7ae7d1d",
"id": "4d9d8321",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -92,7 +92,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "651a542c",
"id": "dcf0e427",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -104,7 +104,7 @@
},
{
"cell_type": "markdown",
"id": "8c33cb81",
"id": "0d4ea2df",
"metadata": {},
"source": [
"We begin by using {py:func}`create_rectangle\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "f363b799",
"id": "f34b0f54",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -130,7 +130,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "cb661546",
"id": "bdbb410f",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -141,7 +141,7 @@
},
{
"cell_type": "markdown",
"id": "dc487858",
"id": "27bb1036",
"metadata": {},
"source": [
"The second argument to {py:class}`functionspace\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "fcc347ea",
"id": "61952105",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -171,7 +171,7 @@
},
{
"cell_type": "markdown",
"id": "cc6eab26",
"id": "96486dc2",
"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": "d4afefff",
"id": "2238d83f",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -191,7 +191,7 @@
},
{
"cell_type": "markdown",
"id": "e09152e1",
"id": "3b1a211c",
"metadata": {},
"source": [
"and use {py:func}`dirichletbc <dolfinx.fem.dirichletbc>` to define the\n",
Expand All @@ -204,7 +204,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "ee568a15",
"id": "a2c8282e",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -215,7 +215,7 @@
},
{
"cell_type": "markdown",
"id": "f4501cc7",
"id": "aca530fa",
"metadata": {},
"source": [
"Next, we express the variational problem using UFL."
Expand All @@ -224,7 +224,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "f2e9553c",
"id": "356b176c",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "6f04926c",
"id": "aa65bed9",
"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": "f973943b",
"id": "16bf6b1d",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "504a5643",
"id": "aaaf9997",
"metadata": {},
"source": [
"### Matrix-free conjugate gradient solver\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "177ef476",
"id": "fbcfbb3b",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "ab7c1b50",
"id": "e7223804",
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -306,7 +306,7 @@
},
{
"cell_type": "markdown",
"id": "0c81c356",
"id": "0bf51315",
"metadata": {
"lines_to_next_cell": 2
},
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{
"cell_type": "code",
"execution_count": null,
"id": "dc34e572",
"id": "086ca5b5",
"metadata": {
"lines_to_next_cell": 2
},
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},
{
"cell_type": "markdown",
"id": "07ed8587",
"id": "ff008238",
"metadata": {
"lines_to_next_cell": 2
},
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{
"cell_type": "code",
"execution_count": null,
"id": "e87889dd",
"id": "fc3a95ed",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "8dd58a01",
"id": "adbc4fe9",
"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": "03b2c957",
"id": "276e029e",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "f5e80f75",
"id": "efd781fd",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "f861ecb7",
"id": "a0bb5fbf",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": null,
"id": "5b519b04",
"id": "e84bfbe8",
"metadata": {},
"outputs": [],
"source": [
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"cells": [
{
"cell_type": "markdown",
"id": "d91a3627",
"id": "5cdab8b6",
"metadata": {},
"source": [
"# Mixed formulation for the Poisson equation"
]
},
{
"cell_type": "markdown",
"id": "a5a3cb48",
"id": "a32e4b53",
"metadata": {},
"source": [
"This demo illustrates how to solve Poisson equation using a mixed\n",
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},
{
"cell_type": "markdown",
"id": "9ab3d597",
"id": "cdf431e3",
"metadata": {},
"source": [
"```{admonition} Download sources\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "94f071e1",
"id": "a4a0dcce",
"metadata": {},
"outputs": [],
"source": [
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1 change: 0 additions & 1 deletion dolfinx/main/python/_modules/dolfinx/fem/function.html
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Expand Up @@ -743,7 +743,6 @@ <h1>Source code for dolfinx.fem.function</h1><div class="highlight"><pre>
<span class="n">form_compiler_options</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="n">form_compiler_options</span><span class="p">[</span><span class="s2">&quot;scalar_type&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">dtype</span>

<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Create element&quot;</span><span class="p">)</span>
<span class="n">cpp_element</span> <span class="o">=</span> <span class="n">_create_dolfinx_element</span><span class="p">(</span><span class="n">mesh</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">cell_type</span><span class="p">,</span> <span class="n">ufl_e</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
<span class="n">cpp_dofmap</span> <span class="o">=</span> <span class="n">_cpp</span><span class="o">.</span><span class="n">fem</span><span class="o">.</span><span class="n">create_dofmap</span><span class="p">(</span><span class="n">mesh</span><span class="o">.</span><span class="n">comm</span><span class="p">,</span> <span class="n">mesh</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">_cpp_object</span><span class="p">,</span> <span class="n">cpp_element</span><span class="p">)</span>

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