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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-b3fde3de-5ee6-4732-9df3-3270c9bd8c1c">
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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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<div class="amsmath math notranslate nohighlight" id="equation-333f7671-eb58-4fd0-85ed-231435af074c">
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<span class="eqno">(1)<a class="headerlink" href="#equation-333f7671-eb58-4fd0-85ed-231435af074c" 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/cpp/doxygen/d0/d47/mesh_2utils_8h.html

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Functions</h2></td></tr>
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<tr class="memitem:a27837f44f6ff45f6809893315743cb38" id="r_a27837f44f6ff45f6809893315743cb38"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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<tr class="memitem:a27837f44f6ff45f6809893315743cb38"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a27837f44f6ff45f6809893315743cb38">reorder_list</a> (std::span&lt; T &gt; list, std::span&lt; const std::int32_t &gt; nodemap)</td></tr>
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<tr class="memdesc:a27837f44f6ff45f6809893315743cb38"><td class="mdescLeft">&#160;</td><td class="mdescRight">Re-order the nodes a fixed-degree adjacency list. <br /></td></tr>
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<tr class="memdesc:a27837f44f6ff45f6809893315743cb38"><td class="mdescLeft">&#160;</td><td class="mdescRight">Re-order the nodes of a fixed-degree adjacency list. <br /></td></tr>
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<tr class="separator:a27837f44f6ff45f6809893315743cb38"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a299052cd10f30e851971964dec00d651" id="r_a299052cd10f30e851971964dec00d651"><td class="memTemplParams" colspan="2">template&lt;std::floating_point T&gt; </td></tr>
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<tr class="memitem:a299052cd10f30e851971964dec00d651"><td class="memTemplItemLeft" align="right" valign="top">std::tuple&lt; std::vector&lt; std::int32_t &gt;, std::vector&lt; T &gt;, std::vector&lt; std::int32_t &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a299052cd10f30e851971964dec00d651">compute_vertex_coords_boundary</a> (const <a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">mesh::Mesh</a>&lt; T &gt; &amp;mesh, int dim, std::span&lt; const std::int32_t &gt; facets)</td></tr>
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<tr class="separator:a94d7b72914936f9a4d6133c0340ac46e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a611ba63b9b9197c08613cccdc41464ee" id="r_a611ba63b9b9197c08613cccdc41464ee"><td class="memTemplParams" colspan="2">template&lt;typename U &gt; </td></tr>
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<tr class="memitem:a611ba63b9b9197c08613cccdc41464ee"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">Mesh</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#a611ba63b9b9197c08613cccdc41464ee">create_mesh</a> (MPI_Comm comm, MPI_Comm commt, std::span&lt; const std::int64_t &gt; cells, const <a class="el" href="../../d9/d35/classdolfinx_1_1fem_1_1CoordinateElement.html">fem::CoordinateElement</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt; &amp;element, MPI_Comm commg, const U &amp;x, std::array&lt; std::size_t, 2 &gt; xshape, const <a class="el" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#acab22e3b5c8ac14664c8cd8e6f53fb70">CellPartitionFunction</a> &amp;partitioner)</td></tr>
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<tr class="memdesc:a611ba63b9b9197c08613cccdc41464ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a distributed mesh wirh a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. <br /></td></tr>
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<tr class="memdesc:a611ba63b9b9197c08613cccdc41464ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a distributed mesh with a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. <br /></td></tr>
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<tr class="separator:a611ba63b9b9197c08613cccdc41464ee"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:ada3471710d7fca68f819993efab03d81" id="r_ada3471710d7fca68f819993efab03d81"><td class="memTemplParams" colspan="2">template&lt;typename U &gt; </td></tr>
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<tr class="memitem:ada3471710d7fca68f819993efab03d81"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">Mesh</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#ada3471710d7fca68f819993efab03d81">create_mesh</a> (MPI_Comm comm, std::span&lt; const std::int64_t &gt; cells, const <a class="el" href="../../d9/d35/classdolfinx_1_1fem_1_1CoordinateElement.html">fem::CoordinateElement</a>&lt; std::remove_reference_t&lt; typename U::value_type &gt; &gt; &amp;elements, const U &amp;x, std::array&lt; std::size_t, 2 &gt; xshape, <a class="el" href="../../dd/d7d/namespacedolfinx_1_1mesh.html#a38d109d131f3180f43267fcf9fe9c4c4">GhostMode</a> ghost_mode)</td></tr>
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<p>Re-order the nodes a fixed-degree adjacency list. </p>
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<p>Re-order the nodes of a fixed-degree adjacency list. </p>
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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,out]</td><td class="paramname">list</td><td>Fixed-degree adjacency list stored row-major. Degree is equal to <code>list.size() / nodemap.size()</code>. </td></tr>

dolfinx/main/cpp/doxygen/d0/d47/mesh_2utils_8h_source.html

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<div class="ttc" id="aclassdolfinx_1_1mesh_1_1Mesh_html"><div class="ttname"><a href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">dolfinx::mesh::Mesh</a></div><div class="ttdoc">A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.</div><div class="ttdef"><b>Definition</b> Mesh.h:23</div></div>
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<div class="ttc" id="aclassdolfinx_1_1mesh_1_1Topology_html"><div class="ttname"><a href="../../da/d02/classdolfinx_1_1mesh_1_1Topology.html">dolfinx::mesh::Topology</a></div><div class="ttdoc">Topology stores the topology of a mesh, consisting of mesh entities and connectivity (incidence relat...</div><div class="ttdef"><b>Definition</b> Topology.h:45</div></div>
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<div class="ttc" id="aconceptdolfinx_1_1mesh_1_1MarkerFn_html"><div class="ttname"><a href="../../da/d7b/conceptdolfinx_1_1mesh_1_1MarkerFn.html">dolfinx::mesh::MarkerFn</a></div><div class="ttdoc">Requirements on function for geometry marking.</div><div class="ttdef"><b>Definition</b> utils.h:469</div></div>
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<div class="ttc" id="amesh_2utils_8h_html_a27837f44f6ff45f6809893315743cb38"><div class="ttname"><a href="../../d0/d47/mesh_2utils_8h.html#a27837f44f6ff45f6809893315743cb38">dolfinx::mesh::impl::reorder_list</a></div><div class="ttdeci">void reorder_list(std::span&lt; T &gt; list, std::span&lt; const std::int32_t &gt; nodemap)</div><div class="ttdoc">Re-order the nodes a fixed-degree adjacency list.</div><div class="ttdef"><b>Definition</b> utils.h:51</div></div>
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<div class="ttc" id="amesh_2utils_8h_html_a27837f44f6ff45f6809893315743cb38"><div class="ttname"><a href="../../d0/d47/mesh_2utils_8h.html#a27837f44f6ff45f6809893315743cb38">dolfinx::mesh::impl::reorder_list</a></div><div class="ttdeci">void reorder_list(std::span&lt; T &gt; list, std::span&lt; const std::int32_t &gt; nodemap)</div><div class="ttdoc">Re-order the nodes of a fixed-degree adjacency list.</div><div class="ttdef"><b>Definition</b> utils.h:51</div></div>
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<div class="ttc" id="amesh_2utils_8h_html_a299052cd10f30e851971964dec00d651"><div class="ttname"><a href="../../d0/d47/mesh_2utils_8h.html#a299052cd10f30e851971964dec00d651">dolfinx::mesh::impl::compute_vertex_coords_boundary</a></div><div class="ttdeci">std::tuple&lt; std::vector&lt; std::int32_t &gt;, std::vector&lt; T &gt;, std::vector&lt; std::int32_t &gt; &gt; compute_vertex_coords_boundary(const mesh::Mesh&lt; T &gt; &amp;mesh, int dim, std::span&lt; const std::int32_t &gt; facets)</div><div class="ttdoc">Compute the coordinates of 'vertices' for entities of a given dimension that are attached to specifie...</div><div class="ttdef"><b>Definition</b> utils.h:82</div></div>
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<div class="ttc" id="amesh_2utils_8h_html_a84f97c83c2ce148b50154b58fa8aea96"><div class="ttname"><a href="../../d0/d47/mesh_2utils_8h.html#a84f97c83c2ce148b50154b58fa8aea96">dolfinx::mesh::impl::compute_vertex_coords</a></div><div class="ttdeci">std::pair&lt; std::vector&lt; T &gt;, std::array&lt; std::size_t, 2 &gt; &gt; compute_vertex_coords(const mesh::Mesh&lt; T &gt; &amp;mesh)</div><div class="ttdoc">The coordinates for all 'vertices' in the mesh.</div><div class="ttdef"><b>Definition</b> utils.h:427</div></div>
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<div class="ttc" id="anamespacedolfinx_1_1MPI_html_a0d292f79536312c2ac410d2353441bc4"><div class="ttname"><a href="../../da/dfe/namespacedolfinx_1_1MPI.html#a0d292f79536312c2ac410d2353441bc4">dolfinx::MPI::distribute_data</a></div><div class="ttdeci">std::vector&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt; distribute_data(MPI_Comm comm0, std::span&lt; const std::int64_t &gt; indices, MPI_Comm comm1, const U &amp;x, int shape1)</div><div class="ttdoc">Distribute rows of a rectangular data array to ranks where they are required (scalable version).</div><div class="ttdef"><b>Definition</b> MPI.h:681</div></div>

dolfinx/main/cpp/doxygen/d9/d93/Topology_8h_source.html

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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">// MPI communicator</span></div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_namespace" href="../../d2/dc7/namespacedolfinx.html">dolfinx</a>::MPI::Comm _comm;</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// Cell types for entites in Topology, as follows:</span></div>
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dolfinx/main/cpp/doxygen/dd/d7d/namespacedolfinx_1_1mesh.html

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<tr class="separator:a94d7b72914936f9a4d6133c0340ac46e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a611ba63b9b9197c08613cccdc41464ee" id="r_a611ba63b9b9197c08613cccdc41464ee"><td class="memTemplParams" colspan="2">template&lt;typename U &gt; </td></tr>
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<tr class="memitem:a611ba63b9b9197c08613cccdc41464ee"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">Mesh</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a611ba63b9b9197c08613cccdc41464ee">create_mesh</a> (MPI_Comm comm, MPI_Comm commt, std::span&lt; const std::int64_t &gt; cells, const <a class="el" href="../../d9/d35/classdolfinx_1_1fem_1_1CoordinateElement.html">fem::CoordinateElement</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt; &amp;element, MPI_Comm commg, const U &amp;x, std::array&lt; std::size_t, 2 &gt; xshape, const <a class="el" href="#acab22e3b5c8ac14664c8cd8e6f53fb70">CellPartitionFunction</a> &amp;partitioner)</td></tr>
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<tr class="memdesc:a611ba63b9b9197c08613cccdc41464ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a distributed mesh wirh a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. <br /></td></tr>
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<tr class="memdesc:a611ba63b9b9197c08613cccdc41464ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a distributed mesh with a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. <br /></td></tr>
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<tr class="memitem:ada3471710d7fca68f819993efab03d81" id="r_ada3471710d7fca68f819993efab03d81"><td class="memTemplParams" colspan="2">template&lt;typename U &gt; </td></tr>
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<tr class="memitem:ada3471710d7fca68f819993efab03d81"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d0/ddf/classdolfinx_1_1mesh_1_1Mesh.html">Mesh</a>&lt; typename std::remove_reference_t&lt; typename U::value_type &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#ada3471710d7fca68f819993efab03d81">create_mesh</a> (MPI_Comm comm, std::span&lt; const std::int64_t &gt; cells, const <a class="el" href="../../d9/d35/classdolfinx_1_1fem_1_1CoordinateElement.html">fem::CoordinateElement</a>&lt; std::remove_reference_t&lt; typename U::value_type &gt; &gt; &amp;elements, const U &amp;x, std::array&lt; std::size_t, 2 &gt; xshape, <a class="el" href="#a38d109d131f3180f43267fcf9fe9c4c4">GhostMode</a> ghost_mode)</td></tr>
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<p>Create a distributed mesh wirh a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. </p>
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<p>Create a distributed mesh with a single cell type from mesh data and using a provided graph partitioning function for determining the parallel distribution of the mesh. </p>
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<p>From mesh input data that is distributed across processes, a distributed <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::Mesh</a> is created. If the partitioning function is not callable, i.e. it does not store a callable function, no re-distribution of cells is done.</p>
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<tr><td class="paramdir">[in]</td><td class="paramname">cells</td><td>Cells, grouped by cell type with <code>cells[i]</code> being the cells of the same type. Cells are defined by their 'nodes' (using global indices) following the Basix ordering, and for each cell type concatenated to form a flattened list. For lowest-order cells this will be just the cell vertices. For higher-order geometry cells, other cell 'nodes' will be included. See <a class="el" href="../../df/dcf/namespacedolfinx_1_1io_1_1cells.html" title="Functions for the re-ordering of input mesh topology to the DOLFINx ordering, and transpose orderings...">io::cells</a> for examples of the Basix ordering. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">elements</td><td>Coordinate elements for the cells, where <code>elements[i]</code> is the coordinate element for the cells in <code>cells[i]</code>. <b>The list of elements must be the same on all calling parallel ranks.</b> </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">commg</td><td>Communicator for geometry. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td><a class="el" href="../../d8/dfb/classdolfinx_1_1mesh_1_1Geometry.html" title="Geometry stores the geometry imposed on a mesh.">Geometry</a> data ('node' coordinates). Row-major storage. The global index of the <code>i</code>th node (row) in <code>x</code> is taken as <code>i</code> plus the paralell rank offset (on <code>comm</code>), where rhe offset is the sum of <code>x</code> rows on all lower ranks than the caller. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td><a class="el" href="../../d8/dfb/classdolfinx_1_1mesh_1_1Geometry.html" title="Geometry stores the geometry imposed on a mesh.">Geometry</a> data ('node' coordinates). Row-major storage. The global index of the <code>i</code>th node (row) in <code>x</code> is taken as <code>i</code> plus the parallel rank offset (on <code>comm</code>), where the offset is the sum of <code>x</code> rows on all lower ranks than the caller. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">entities</td><td>Indices of entities in <code>mesh</code> to include in the sub-mesh. </td></tr>
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