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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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<span class="eqno">(1)<a class="headerlink" href="#equation-f25ec5ad-5a86-4e10-8b74-a0777d57f79c" title="Permalink to this equation"></a></span>\[\begin{align}
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<span class="eqno">(1)<a class="headerlink" href="#equation-b3fde3de-5ee6-4732-9df3-3270c9bd8c1c" 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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dolfinx/main/cpp/doxygen/d0/d47/mesh_2utils_8h.html

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dolfinx/main/cpp/doxygen/d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html

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<tr class="memitem:a721db5305d75e87ce96e0f3b248c546a" id="r_a721db5305d75e87ce96e0f3b248c546a"><td class="memTemplParams" colspan="2">template&lt;typename V &gt; <br />
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requires std::is_convertible_v&lt;std::remove_cvref_t&lt;V&gt;, <a class="el" href="../../d8/dfb/classdolfinx_1_1mesh_1_1Geometry.html">Geometry</a>&lt;T&gt;&gt;</td></tr>
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<tr class="memitem:a721db5305d75e87ce96e0f3b248c546a"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a721db5305d75e87ce96e0f3b248c546a">Mesh</a> (MPI_Comm <a class="el" href="#ad3217ebf3e21d7902bf89ab1248dabb9">comm</a>, std::shared_ptr&lt; <a class="el" href="../../da/d02/classdolfinx_1_1mesh_1_1Topology.html">Topology</a> &gt; <a class="el" href="#a2bbad0fc0865a08f09a59ac125a07a5a">topology</a>, V &amp;&amp;<a class="el" href="#a66440f67948f04ee83e4f5a797f08856">geometry</a>)</td></tr>
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<tr class="memdesc:a721db5305d75e87ce96e0f3b248c546a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a mesh. <br /></td></tr>
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<tr class="memdesc:a721db5305d75e87ce96e0f3b248c546a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a <a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a>. <br /></td></tr>
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<tr class="separator:a721db5305d75e87ce96e0f3b248c546a"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a3c17bd158a5a57d0bce9d764f21b640e" id="r_a3c17bd158a5a57d0bce9d764f21b640e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a3c17bd158a5a57d0bce9d764f21b640e">Mesh</a> (const <a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">Mesh</a> &amp;mesh)=default</td></tr>
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<tr class="memdesc:a2bbad0fc0865a08f09a59ac125a07a5a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get mesh topology. <br /></td></tr>
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<tr class="separator:a2bbad0fc0865a08f09a59ac125a07a5a"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:ad8296e987ca22235c0238ff82e2ec153" id="r_ad8296e987ca22235c0238ff82e2ec153"><td class="memItemLeft" align="right" valign="top">std::shared_ptr&lt; const <a class="el" href="../../da/d02/classdolfinx_1_1mesh_1_1Topology.html">Topology</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad8296e987ca22235c0238ff82e2ec153">topology</a> () const</td></tr>
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<tr class="memdesc:ad8296e987ca22235c0238ff82e2ec153"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get mesh topology (const version). <br /></td></tr>
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<tr class="separator:ad8296e987ca22235c0238ff82e2ec153"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a0a2cf2ebf198cd471ba4bffdad8d58a4" id="r_a0a2cf2ebf198cd471ba4bffdad8d58a4"><td class="memItemLeft" align="right" valign="top">std::shared_ptr&lt; <a class="el" href="../../da/d02/classdolfinx_1_1mesh_1_1Topology.html">Topology</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a0a2cf2ebf198cd471ba4bffdad8d58a4">topology_mutable</a> () const</td></tr>
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<tr class="memdesc:a0a2cf2ebf198cd471ba4bffdad8d58a4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get mesh topology if one really needs the mutable version. <br /></td></tr>
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<tr class="separator:a0a2cf2ebf198cd471ba4bffdad8d58a4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a66440f67948f04ee83e4f5a797f08856" id="r_a66440f67948f04ee83e4f5a797f08856"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d8/dfb/classdolfinx_1_1mesh_1_1Geometry.html">Geometry</a>&lt; T &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a66440f67948f04ee83e4f5a797f08856">geometry</a> ()</td></tr>
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<tr class="separator:a66440f67948f04ee83e4f5a797f08856"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a2ac19454b231641e82cfec036ece0d4a" id="r_a2ac19454b231641e82cfec036ece0d4a"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="../../d8/dfb/classdolfinx_1_1mesh_1_1Geometry.html">Geometry</a>&lt; T &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a2ac19454b231641e82cfec036ece0d4a">geometry</a> () const</td></tr>
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<tr class="memdesc:a2ac19454b231641e82cfec036ece0d4a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get mesh geometry (const version) <br /></td></tr>
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<tr class="memdesc:a2ac19454b231641e82cfec036ece0d4a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get mesh geometry (const version). <br /></td></tr>
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<tr class="separator:a2ac19454b231641e82cfec036ece0d4a"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:ad3217ebf3e21d7902bf89ab1248dabb9" id="r_ad3217ebf3e21d7902bf89ab1248dabb9"><td class="memItemLeft" align="right" valign="top">MPI_Comm&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad3217ebf3e21d7902bf89ab1248dabb9">comm</a> () const</td></tr>
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<tr class="memdesc:ad3217ebf3e21d7902bf89ab1248dabb9"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> <a class="el" href="../../da/dfe/namespacedolfinx_1_1MPI.html" title="MPI support functionality.">MPI</a> communicator. <br /></td></tr>
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class dolfinx::mesh::Mesh&lt; T &gt;</div><p>A <a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> consists of a set of connected and numbered mesh topological entities, and geometry data. </p>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">The</td><td>floating point type for representing the geometry. </td></tr>
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<tr><td class="paramname">Floating</td><td>point type for representing the geometry. </td></tr>
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<p>Create a mesh. </p>
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<p>Create a <a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a>. </p>
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<dl class="section note"><dt>Note</dt><dd>This constructor is not normally called by users. User code will normally use <a class="el" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#a94d7b72914936f9a4d6133c0340ac46e" title="Create a distributed mesh::Mesh from mesh data and using the provided graph partitioning function for...">create_mesh</a>.</dd></dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">comm</td><td><a class="el" href="../../da/dfe/namespacedolfinx_1_1MPI.html" title="MPI support functionality.">MPI</a> Communicator </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">topology</td><td><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> topology </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">geometry</td><td><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> geometry </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">comm</td><td><a class="el" href="../../da/dfe/namespacedolfinx_1_1MPI.html" title="MPI support functionality.">MPI</a> Communicator. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">topology</td><td><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> topology. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">geometry</td><td><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html" title="A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.">Mesh</a> geometry. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The communicator on which the mesh is distributed </dd></dl>
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dolfinx/main/cpp/doxygen/d1/d7e/graphbuild_8h_source.html

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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span>{</div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">enum class</span> <a class="code hl_enumeration" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#ac3c2cbbef08f3b7ddc3b06c6bd5a2271">CellType</a>;</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">const</span> std::vector&lt;std::span&lt;const std::int64_t&gt;&gt;&amp; cells);</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">const</span> std::vector&lt;std::span&lt;const std::int64_t&gt;&gt;&amp; cells);</div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html">dolfinx::mesh</a></div><div class="ttdoc">Mesh data structures and algorithms on meshes.</div><div class="ttdef"><b>Definition</b> DofMap.h:32</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html_aab5c2d292165f0f24be6db01db324529"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html#aab5c2d292165f0f24be6db01db324529">dolfinx::mesh::build_local_dual_graph</a></div><div class="ttdeci">std::tuple&lt; graph::AdjacencyList&lt; std::int32_t &gt;, std::vector&lt; std::int64_t &gt;, std::size_t, std::vector&lt; std::int32_t &gt; &gt; build_local_dual_graph(std::span&lt; const CellType &gt; celltypes, const std::vector&lt; std::span&lt; const std::int64_t &gt; &gt; &amp;cells)</div><div class="ttdoc">Compute the local part of the dual graph (cell-cell connections via facets) and facets with only one ...</div><div class="ttdef"><b>Definition</b> graphbuild.cpp:354</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html_ac3c2cbbef08f3b7ddc3b06c6bd5a2271"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html#ac3c2cbbef08f3b7ddc3b06c6bd5a2271">dolfinx::mesh::CellType</a></div><div class="ttdeci">CellType</div><div class="ttdoc">Cell type identifier.</div><div class="ttdef"><b>Definition</b> cell_types.h:22</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html_ac4ecab159304e7a6c7146533196aca6f"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html#ac4ecab159304e7a6c7146533196aca6f">dolfinx::mesh::build_dual_graph</a></div><div class="ttdeci">graph::AdjacencyList&lt; std::int64_t &gt; build_dual_graph(MPI_Comm comm, std::span&lt; const CellType &gt; celltypes, const std::vector&lt; std::span&lt; const std::int64_t &gt; &gt; &amp;cells)</div><div class="ttdoc">Build distributed mesh dual graph (cell-cell connections via facets) from minimal mesh data.</div><div class="ttdef"><b>Definition</b> graphbuild.cpp:518</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1mesh_html_ac4ecab159304e7a6c7146533196aca6f"><div class="ttname"><a href="../../dd/d7d/namespacedolfinx_1_1mesh.html#ac4ecab159304e7a6c7146533196aca6f">dolfinx::mesh::build_dual_graph</a></div><div class="ttdeci">graph::AdjacencyList&lt; std::int64_t &gt; build_dual_graph(MPI_Comm comm, std::span&lt; const CellType &gt; celltypes, const std::vector&lt; std::span&lt; const std::int64_t &gt; &gt; &amp;cells)</div><div class="ttdoc">Build distributed mesh dual graph (cell-cell connections via facets) from minimal mesh data.</div><div class="ttdef"><b>Definition</b> graphbuild.cpp:519</div></div>
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