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<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.22/docs"> 3.22</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.21/docs"> 3.21</a></li>
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<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.18/docs"> 3.18</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.17/docs"> 3.17</a></li>
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<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.10/docs"> 3.10</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.9/docs"> 3.9</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.8/docs"> 3.8</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.7/docs"> 3.7</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.6/docs"> 3.6</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.5/docs"> 3.5</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.4/docs"> 3.4</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.3/docs"> 3.3</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="dmplex-unstructured-grids">
<span id="ch-unstructured"></span><h1>DMPlex: Unstructured Grids<a class="headerlink" href="#dmplex-unstructured-grids" title="Link to this heading">#</a></h1>
<p>This chapter introduces the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> subclass of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>, which allows
the user to handle unstructured grids (or meshes) using the generic <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> interface
for hierarchy and multi-physics. <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> was created to remedy a huge
problem in all current PDE simulation codes, namely that the
discretization was so closely tied to the data layout and solver that
switching discretizations in the same code was not possible. Not only
does this preclude the kind of comparison that is necessary for
scientific investigation, but it makes library (as opposed to monolithic
application) development impossible.</p>
<section id="representing-unstructured-grids">
<h2>Representing Unstructured Grids<a class="headerlink" href="#representing-unstructured-grids" title="Link to this heading">#</a></h2>
<p>The main advantage of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> in representing topology is that it
treats all the different pieces of a mesh, e.g. cells, faces, edges, and
vertices, in the same way. This allows the interface to be
small and simple, while remaining flexible and general. This also allows
“dimension independent programming”, which means that the same algorithm
can be used unchanged for meshes of different shapes and dimensions.</p>
<p>All pieces of the mesh (vertices, edges, faces, and cells) are treated as <em>points</em> (or mesh entities), which are each identified by a
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span></code>. A mesh is built by relating points to other points, in
particular specifying a “covering” relation among the points. For
example, an edge is defined by being covered by two vertices, and a
triangle can be defined by being covered by three edges (or even by
three vertices). This structure is known as a <a class="reference external" href="http://en.wikipedia.org/wiki/Hasse_diagram">Hasse Diagram</a>, which is a
Directed Acyclic Graph (DAG) representing a cell complex using the
covering relation. The graph edges represent the relation, which also
encodes a partially ordered set (poset).</p>
<p>For example, we can encode the doublet mesh as in <a class="reference internal" href="#fig-doubletmesh"><span class="std std-numref">Fig. 8</span></a>,</p>
<figure class="align-default" id="fig-doubletmesh">
<img alt="../_images/dmplex_doublet_mesh.svg" src="../_images/dmplex_doublet_mesh.svg" /><figcaption>
<p><span class="caption-number">Fig. 8 </span><span class="caption-text">A 2D doublet mesh, two triangles sharing an edge.</span><a class="headerlink" href="#fig-doubletmesh" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>which can also be represented as the DAG in
<a class="reference internal" href="#fig-doubletdag"><span class="std std-numref">Fig. 9</span></a>.</p>
<figure class="align-default" id="fig-doubletdag">
<img alt="../_images/dmplex_doublet_dag.svg" src="../_images/dmplex_doublet_dag.svg" /><figcaption>
<p><span class="caption-number">Fig. 9 </span><span class="caption-text">The Hasse diagram for our 2D doublet mesh, expressed as a DAG.</span><a class="headerlink" href="#fig-doubletdag" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>To use the PETSc API, we consecutively number the mesh pieces. The
PETSc convention in 3 dimensions is to number first cells, then
vertices, then faces, and then edges. In 2 dimensions the convention is
to number faces, vertices, and then edges.
In terms of the labels in
<a class="reference internal" href="#fig-doubletmesh"><span class="std std-numref">Fig. 8</span></a>, these numberings are</p>
<div class="math">
\[
f_0 \mapsto \mathtt{0}, f_1 \mapsto \mathtt{1}, \\ v_0 \mapsto \mathtt{2}, v_1 \mapsto \mathtt{3}, v_2 \mapsto \mathtt{4}, v_3 \mapsto \mathtt{5}, \\ e_0 \mapsto \mathtt{6}, e_1 \mapsto \mathtt{7}, e_2 \mapsto \mathtt{8}, e_3 \mapsto \mathtt{9}, e_4 \mapsto \mathtt{10}
\]</div>
<p>First, we declare the set of points present in a mesh,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexSetChart.html">DMPlexSetChart</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">11</span><span class="p">);</span>
</pre></div>
</div>
<p>Note that a <em>chart</em> here corresponds to a semi-closed interval (e.g
<span class="math">\([0,11) = \{0,1,\ldots,10\}\)</span>) specifying the range of indices we’d
like to use to define points on the current rank. We then define the
covering relation, which we call the <em>cone</em>, which are also the in-edges
in the DAG. In order to preallocate correctly, we first provide sizes,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="cm">/* <a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a>(dm, point, number of points that cover the point); */</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMSetUp.html">DMSetUp</a></span><span class="p">(</span><span class="n">dm</span><span class="p">);</span>
</pre></div>
</div>
<p>and then point values (recall each point is an integer that represents a single geometric entity, a cell, face, edge, or vertex),</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="cm">/* <a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a>(dm, point, [points that cover the point]); */</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">]);</span>
</pre></div>
</div>
<p>There is also an API for providing the dual relation, using
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetSupportSize.html">DMPlexSetSupportSize</a>()</span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetSupport.html">DMPlexSetSupport</a>()</span></code>, but this can be
calculated automatically using the provided <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetConeSize.html">DMPlexSetConeSize</a>()</span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetCone.html">DMPlexSetCone</a>()</span></code> information and then calling</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexSymmetrize.html">DMPlexSymmetrize</a></span><span class="p">(</span><span class="n">dm</span><span class="p">);</span>
</pre></div>
</div>
<p>The “symmetrization” is in the sense of the DAG. Each point knows its covering (cone) and each point knows what it covers (support). Note that when using automatic symmetrization, cones will be ordered but supports will not. The user can enforce an ordering on supports by rewriting them after symmetrization using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetSupport.html">DMPlexSetSupport</a>()</span></code>.</p>
<p>In order to support efficient queries, we construct fast
search structures and indices for the different types of points using</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexStratify.html">DMPlexStratify</a></span><span class="p">(</span><span class="n">dm</span><span class="p">);</span>
</pre></div>
</div>
</section>
<section id="grid-point-orientations">
<h2>Grid Point Orientations<a class="headerlink" href="#grid-point-orientations" title="Link to this heading">#</a></h2>
<p>TODO: fill this out with regard to orientations.</p>
<p>Should probably reference Hapla and summarize what’s there.</p>
</section>
<section id="dealing-with-periodicity">
<h2>Dealing with Periodicity<a class="headerlink" href="#dealing-with-periodicity" title="Link to this heading">#</a></h2>
<p>Plex allows you to represent periodic domains is two ways. Using the default scheme, periodic topology can be represented directly. This ensures that all topological queries can be satisfied, but then care must be taken in representing functions over the mesh, such as the coordinates. The second method is to use a non-periodic topology, but connect certain mesh points using the local-to-global map for that DM. This allows a more general set of mappings to be implemented, such as partial twists, but topological queries on the periodic boundary cease to function.</p>
<p>For the default scheme, a call to <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMLocalizeCoordinates.html">DMLocalizeCoordinates</a>()</span></code> (which usually happens automatically on mesh creation) creates a second, discontinuous coordinate field. These values can be accessed using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetCellCoordinates.html">DMGetCellCoordinates</a>()</span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetCellCoordinatesLocal.html">DMGetCellCoordinatesLocal</a>()</span></code>. Plex provides a convenience method, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetCellCoordinates.html">DMPlexGetCellCoordinates</a>()</span></code>, that extracts cell coordinates correctly, depending on the periodicity of the mesh. An example of its use is shown below:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="k">const</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="o">*</span><span class="n">array</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="o">*</span><span class="n">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">numCoords</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscBool.html">PetscBool</a></span><span class="w"> </span><span class="n">isDG</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DMPlex/DMPlexGetCellCoordinates.html">DMPlexGetCellCoordinates</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">isDG</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">numCoords</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">array</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">coords</span><span class="p">));</span>
<span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">cc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">cc</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">numCoords</span><span class="o">/</span><span class="n">dim</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">cc</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cc</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">" -- "</span><span class="p">));</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">"("</span><span class="p">));</span>
<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">dim</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">d</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">d</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">", "</span><span class="p">));</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">"%g"</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n"><a href="../manualpages/Sys/PetscRealPart.html">PetscRealPart</a></span><span class="p">(</span><span class="n">coords</span><span class="p">[</span><span class="n">cc</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">dim</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">d</span><span class="p">])));</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">")"</span><span class="p">));</span>
<span class="p">}</span>
<span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscPrintf.html">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="p">));</span>
<span class="n"><a href="../manualpages/Sys/PetscCall.html">PetscCall</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DMPlex/DMPlexRestoreCellCoordinates.html">DMPlexRestoreCellCoordinates</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">isDG</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">numCoords</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">array</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">coords</span><span class="p">));</span>
</pre></div>
</div>
</section>
<section id="connecting-grids-to-data-using-petscsection">
<h2>Connecting Grids to Data Using PetscSection:<a class="headerlink" href="#connecting-grids-to-data-using-petscsection" title="Link to this heading">#</a></h2>
<p>A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is used to describe the connection between the grid and data associated with the grid.
Specifically, it assigns a number of dofs to each mesh entity on the DAG.
See <a class="reference internal" href="section.html#ch-petscsection"><span class="std std-ref">PetscSection: Connecting Grids to Data</span></a> for more details.
Using the mesh from <a class="reference internal" href="#fig-doubletmesh"><span class="std std-numref">Fig. 8</span></a>, we provide an example of creating a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> for a single field.
We can lay out data for a continuous Galerkin <span class="math">\(P_3\)</span> finite element method,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">pStart</span><span class="p">,</span><span class="w"> </span><span class="n">pEnd</span><span class="p">,</span><span class="w"> </span><span class="n">cStart</span><span class="p">,</span><span class="w"> </span><span class="n">cEnd</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="n">vStart</span><span class="p">,</span><span class="w"> </span><span class="n">vEnd</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="n">eStart</span><span class="p">,</span><span class="w"> </span><span class="n">eEnd</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetChart.html">DMPlexGetChart</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">pStart</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">pEnd</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetHeightStratum.html">DMPlexGetHeightStratum</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">cStart</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">cEnd</span><span class="p">);</span><span class="w"> </span><span class="c1">// cells</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetHeightStratum.html">DMPlexGetHeightStratum</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">eStart</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">eEnd</span><span class="p">);</span><span class="w"> </span><span class="c1">// edges</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetHeightStratum.html">DMPlexGetHeightStratum</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">vStart</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">vEnd</span><span class="p">);</span><span class="w"> </span><span class="c1">// vertices, equivalent to <a href="../manualpages/DMPlex/DMPlexGetDepthStratum.html">DMPlexGetDepthStratum</a>(dm, 0, &vStart, &vEnd);</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionSetChart.html">PetscSectionSetChart</a></span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">pStart</span><span class="p">,</span><span class="w"> </span><span class="n">pEnd</span><span class="p">);</span>
<span class="k">for</span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cStart</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">cEnd</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">c</span><span class="p">)</span>
<span class="w"> </span><span class="n"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a></span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<span class="k">for</span><span class="p">(</span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vStart</span><span class="p">;</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">vEnd</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">v</span><span class="p">)</span>
<span class="w"> </span><span class="n"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a></span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<span class="k">for</span><span class="p">(</span><span class="n">e</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">eStart</span><span class="p">;</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">eEnd</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">e</span><span class="p">)</span>
<span class="w"> </span><span class="n"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a></span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// two dof on each edge</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a></span><span class="p">(</span><span class="n">s</span><span class="p">);</span>
</pre></div>
</div>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetHeightStratum.html">DMPlexGetHeightStratum</a>()</span></code> returns all the points of the requested height
in the DAG. Since this problem is in two dimensions the edges are at
height 1 and the vertices at height 2 (the cells are always at height
0). One can also use <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetDepthStratum.html">DMPlexGetDepthStratum</a>()</span></code> to use the depth in the
DAG to select the points. <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetDepth.html">DMPlexGetDepth</a>(dm,&depth)</span></code> returns the depth
of the DAG, hence <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetDepthStratum.html">DMPlexGetDepthStratum</a>(dm,depth-1-h,)</span></code> returns the
same values as <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexGetHeightStratum.html">DMPlexGetHeightStratum</a>(dm,h,)</span></code>.</p>
<p>For <span class="math">\(P_3\)</span> elements there is one degree of freedom at each vertex, 2 along
each edge (resulting in a total of 4 degrees of freedom along each edge
including the vertices, thus being able to reproduce a cubic function)
and 1 degree of freedom within the cell (the bubble function which is
zero along all edges).</p>
<p>Now a PETSc local vector can be created manually using this layout,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/PetscSection/PetscSectionGetStorageSize.html">PetscSectionGetStorageSize</a></span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Vec/VecSetSizes.html">VecSetSizes</a></span><span class="p">(</span><span class="n">localVec</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PETSC_DETERMINE.html">PETSC_DETERMINE</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/Vec/VecSetFromOptions.html">VecSetFromOptions</a></span><span class="p">(</span><span class="n">localVec</span><span class="p">);</span>
</pre></div>
</div>
<p>When working with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/FE/PetscFE.html">PetscFE</a></span></code> (see below) one can simply get the sections (and related vectors) with</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DMSetLocalSection.html">DMSetLocalSection</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMGetLocalVector.html">DMGetLocalVector</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">localVec</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMGetGlobalVector.html">DMGetGlobalVector</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">globalVec</span><span class="p">);</span>
</pre></div>
</div>
<section id="dmplex-specific-petscsection-features">
<h3>DMPlex-specific PetscSection Features:<a class="headerlink" href="#dmplex-specific-petscsection-features" title="Link to this heading">#</a></h3>
<p>The following features are built into <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>.
However, their usage and purpose is best understood through <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code>.</p>
<section id="closure">
<h4>Closure:<a class="headerlink" href="#closure" title="Link to this heading">#</a></h4>
<p>Closure information can be attached to a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> to allow for more efficient closure information queries.
This information can either be set directly with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexCreateClosureIndex.html">DMPlexCreateClosureIndex</a>()</span></code> or generated automatically for a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexCreateClosureIndex.html">DMPlexCreateClosureIndex</a>()</span></code>.</p>
</section>
<section id="symmetries-accessing-data-from-different-orientations">
<h4>Symmetries: Accessing data from different orientations<a class="headerlink" href="#symmetries-accessing-data-from-different-orientations" title="Link to this heading">#</a></h4>
<p>While mesh point orientation information specifies how one mesh point is oriented with respect to another, it does not describe how the dofs associated with that mesh point should be permuted for that orientation.
This information is supplied via a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSym.html">PetscSectionSym</a></span></code> object that is attached to the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>.
Generally the setup and usage of this information is handled automatically by PETSc during setup of a Plex using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/FE/PetscFE.html">PetscFE</a></span></code>.</p>
</section>
<section id="closure-permutation">
<h4>Closure Permutation:<a class="headerlink" href="#closure-permutation" title="Link to this heading">#</a></h4>
<p>A permutation of the dof closure of a k-cell may be specified.
This allows data to be returned in an order that might be more efficiently processed than the default (breadth-first search) ordering.
For example, for tensor cells such as quadrilaterals, closure data can be permuted to lexicographic order (i.e. a tensor-product ordering).
This is most commonly done via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSetClosurePermutationTensor.html">DMPlexSetClosurePermutationTensor</a>()</span></code>.
Custom permutations can be set using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetClosurePermutation.html">PetscSectionSetClosurePermutation</a>()</span></code>.</p>
</section>
</section>
</section>
<section id="data-layout-using-dmplex-and-petscfe">
<h2>Data Layout using DMPLEX and PetscFE<a class="headerlink" href="#data-layout-using-dmplex-and-petscfe" title="Link to this heading">#</a></h2>
<p>A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> can automatically create the local section if given a description of the discretization, for example using a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/FE/PetscFE.html">PetscFE</a></span></code> object. We demonstrate this by creating
a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/FE/PetscFE.html">PetscFE</a></span></code> that can be configured from the command line. It is a single, scalar field, and is added to the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMSetField.html">DMSetField</a>()</span></code>.
When a local or global vector is requested, the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> builds the local and global sections automatically.</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexIsSimplex.html">DMPlexIsSimplex</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">simplex</span><span class="p">);</span>
<span class="n"><a href="../manualpages/FE/PetscFECreateDefault.html">PetscFECreateDefault</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_SELF.html">PETSC_COMM_SELF</a></span><span class="p">,</span><span class="w"> </span><span class="n">dim</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">simplex</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">fe</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMSetField.html">DMSetField</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="w"> </span><span class="n">fe</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMCreateDS.html">DMCreateDS</a></span><span class="p">(</span><span class="n">dm</span><span class="p">);</span>
</pre></div>
</div>
<p>Here the call to <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMSetField.html">DMSetField</a>()</span></code> declares the discretization will have one field with the integer label 0 that has one degree of freedom at each point on the <code class="docutils notranslate"><span class="pre">DMPlex</span></code>.
To get the <span class="math">\(P_3\)</span> section above, we can either give the option <code class="docutils notranslate"><span class="pre">-petscspace_degree</span> <span class="pre">3</span></code>, or call <code class="docutils notranslate"><span class="pre"><a href="../manualpages/FE/PetscFECreateLagrange.html">PetscFECreateLagrange</a>()</span></code> and set the degree directly.</p>
</section>
<section id="partitioning-and-ordering">
<h2>Partitioning and Ordering<a class="headerlink" href="#partitioning-and-ordering" title="Link to this heading">#</a></h2>
<p>In the same way as <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MatPartitioning.html">MatPartitioning</a></span></code> or
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/MatGraphOperations/MatGetOrdering.html">MatGetOrdering</a>()</span></code>, give the results of a partitioning or ordering of a graph defined by a sparse matrix,
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/PetscPartitionerDMPlexPartition.html">PetscPartitionerDMPlexPartition</a></span></code> or <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexPermute.html">DMPlexPermute</a></span></code> are encoded in
an <code class="docutils notranslate"><span class="pre"><a href="../manualpages/IS/IS.html">IS</a></span></code>. However, the graph is not the adjacency graph of the matrix
but the mesh itself. Once the mesh is partitioned and
reordered, the data layout from a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> can be used to
automatically derive a problem partitioning/ordering.</p>
<section id="influence-of-variables-on-one-another">
<h3>Influence of Variables on One Another<a class="headerlink" href="#influence-of-variables-on-one-another" title="Link to this heading">#</a></h3>
<p>The Jacobian of a problem represents the influence of some
variable on other variables in the problem. Very often, this influence
pattern is determined jointly by the computational mesh and
discretization. <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMCreateMatrix.html">DMCreateMatrix</a>()</span></code> must compute this pattern when it
automatically creates the properly preallocated Jacobian matrix. In
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code> the influence pattern, or what we will call variable
<em>adjacency</em>, depends only on the stencil since the topology is Cartesian
and the discretization is implicitly finite difference.</p>
<p>In <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code>,
we allow the user to specify the adjacency topologically, while
maintaining good defaults. The pattern is controlled by two flags. The first flag, <code class="docutils notranslate"><span class="pre">useCone</span></code>,
indicates whether variables couple first to their boundary <a class="footnote-reference brackets" href="#boundary-footnote" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>
and then to
neighboring entities, or the reverse. For example, in finite elements,
the variables couple to the set of neighboring cells containing the mesh
point, and we set the flag to <code class="docutils notranslate"><span class="pre">useCone</span> <span class="pre">=</span> <span class="pre"><a href="../manualpages/Sys/PETSC_FALSE.html">PETSC_FALSE</a></span></code>. By contrast,
in finite volumes, cell variables first couple to the cell boundary, and
then to the neighbors, so we set the flag to <code class="docutils notranslate"><span class="pre">useCone</span> <span class="pre">=</span> <span class="pre"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span></code>.
The second flag, <code class="docutils notranslate"><span class="pre">useClosure</span></code>, indicates whether we consider the
transitive closure of the neighbor relation above, or just a single
level. For example, in finite elements, the entire boundary of any cell
couples to the interior, and we set the flag to
<code class="docutils notranslate"><span class="pre">useClosure</span> <span class="pre">=</span> <span class="pre"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span></code>. By contrast, in most finite volume methods,
cells couple only across faces, and not through vertices, so we set the
flag to <code class="docutils notranslate"><span class="pre">useClosure</span> <span class="pre">=</span> <span class="pre"><a href="../manualpages/Sys/PETSC_FALSE.html">PETSC_FALSE</a></span></code>. However, the power of this method
is its flexibility. If we wanted a finite volume method that coupled all
cells around a vertex, we could easily prescribe that by changing to
<code class="docutils notranslate"><span class="pre">useClosure</span> <span class="pre">=</span> <span class="pre"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span></code>.</p>
</section>
</section>
<section id="evaluating-residuals">
<h2>Evaluating Residuals<a class="headerlink" href="#evaluating-residuals" title="Link to this heading">#</a></h2>
<p>The evaluation of a residual or Jacobian, for most discretizations has
the following general form:</p>
<ul class="simple">
<li><p>Traverse the mesh, picking out pieces (which in general overlap),</p></li>
<li><p>Extract some values from the current solution vector, associated with this
piece,</p></li>
<li><p>Calculate some values for the piece, and</p></li>
<li><p>Insert these values into the residual vector</p></li>
</ul>
<p>DMPlex separates these different concerns by passing sets of points from mesh traversal routines to data
extraction routines and back. In this way, the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> which
structures the data inside a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> does not need to know anything
about the mesh inside a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code>.</p>
<p>The most common mesh traversal is the transitive closure of a point,
which is exactly the transitive closure of a point in the DAG using the
covering relation. In other words, the transitive closure consists of
all points that cover the given point (generally a cell) plus all points
that cover those points, etc. So in 2d the transitive closure for a cell
consists of edges and vertices while in 3d it consists of faces, edges,
and vertices. Note that this closure can be calculated orienting the
arrows in either direction. For example, in a finite element
calculation, we calculate an integral over each element, and then sum up
the contributions to the basis function coefficients. The closure of the
element can be expressed discretely as the transitive closure of the
element point in the mesh DAG, where each point also has an orientation.
Then we can retrieve the data using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> methods,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="o">*</span><span class="n">a</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">numPoints</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">points</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Vec/VecGetArrayRead.html">VecGetArrayRead</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="o">&</span><span class="n">a</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetTransitiveClosure.html">DMPlexGetTransitiveClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="n">cell</span><span class="p">,</span><span class="n"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span><span class="p">,</span><span class="o">&</span><span class="n">numPoints</span><span class="p">,</span><span class="o">&</span><span class="n">points</span><span class="p">);</span>
<span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">numPoints</span><span class="o">*</span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">dof</span><span class="p">,</span><span class="w"> </span><span class="n">off</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../manualpages/PetscSection/PetscSectionGetDof.html">PetscSectionGetDof</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="n">p</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">dof</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../manualpages/PetscSection/PetscSectionGetOffset.html">PetscSectionGetOffset</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="n">p</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">off</span><span class="p">);</span>
<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">dof</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">d</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">myfunc</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">off</span><span class="o">+</span><span class="n">d</span><span class="p">]);</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexRestoreTransitiveClosure.html">DMPlexRestoreTransitiveClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">numPoints</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">points</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Vec/VecRestoreArrayRead.html">VecRestoreArrayRead</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">a</span><span class="p">);</span>
</pre></div>
</div>
<p>This operation is so common that we have built a convenience method
around it which returns the values in a contiguous array, correctly
taking into account the orientations of various mesh points:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="k">const</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="o">*</span><span class="n">values</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">csize</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexVecGetClosure.html">DMPlexVecGetClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">csize</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">values</span><span class="p">);</span>
<span class="c1">// Do integral in quadrature loop putting the result into r[]</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexVecRestoreClosure.html">DMPlexVecRestoreClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">csize</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">values</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexVecSetClosure.html">DMPlexVecSetClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">residual</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/ADD_VALUES.html">ADD_VALUES</a></span><span class="p">);</span>
</pre></div>
</div>
<p>A simple example of this kind of calculation is in
<code class="docutils notranslate"><span class="pre">DMPlexComputeL2Diff_Plex()</span></code> (<a href="../src/dm/impls/plex/plexfem.c.html#DMComputeL2Diff_Plex">source</a>).
Note that there is no restriction on the type of cell or dimension of
the mesh in the code above, so it will work for polyhedral cells, hybrid
meshes, and meshes of any dimension, without change. We can also reverse
the covering relation, so that the code works for finite volume methods
where we want the data from neighboring cells for each face:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="o">*</span><span class="n">a</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="mi">2</span><span class="p">],</span><span class="w"> </span><span class="n">numPoints</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">,</span><span class="w"> </span><span class="n">dofA</span><span class="p">,</span><span class="w"> </span><span class="n">offA</span><span class="p">,</span><span class="w"> </span><span class="n">dofB</span><span class="p">,</span><span class="w"> </span><span class="n">offB</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Vec/VecGetArray.html">VecGetArray</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">a</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexGetTransitiveClosure.html">DMPlexGetTransitiveClosure</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">cell</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PETSC_FALSE.html">PETSC_FALSE</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">numPoints</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">points</span><span class="p">);</span>
<span class="n">assert</span><span class="p">(</span><span class="n">numPoints</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionGetDof.html">PetscSectionGetDof</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="mi">0</span><span class="o">*</span><span class="mi">2</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">dofA</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionGetDof.html">PetscSectionGetDof</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="mi">1</span><span class="o">*</span><span class="mi">2</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">dofB</span><span class="p">);</span>
<span class="n">assert</span><span class="p">(</span><span class="n">dofA</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">dofB</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionGetOffset.html">PetscSectionGetOffset</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="mi">0</span><span class="o">*</span><span class="mi">2</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">offA</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSection/PetscSectionGetOffset.html">PetscSectionGetOffset</a></span><span class="p">(</span><span class="n">section</span><span class="p">,</span><span class="w"> </span><span class="n">points</span><span class="p">[</span><span class="mi">1</span><span class="o">*</span><span class="mi">2</span><span class="p">],</span><span class="w"> </span><span class="o">&</span><span class="n">offB</span><span class="p">);</span>
<span class="n">myfunc</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">offA</span><span class="p">],</span><span class="w"> </span><span class="n">a</span><span class="p">[</span><span class="n">offB</span><span class="p">]);</span>
<span class="n"><a href="../manualpages/Vec/VecRestoreArray.html">VecRestoreArray</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">a</span><span class="p">);</span>
</pre></div>
</div>
<p>This kind of calculation is used in
<a href="../src/ts/tutorials/ex11.c.html">TS Tutorial ex11</a>.</p>
</section>
<section id="saving-and-loading-dmplex-data-with-hdf5">
<h2>Saving and Loading DMPlex Data with HDF5<a class="headerlink" href="#saving-and-loading-dmplex-data-with-hdf5" title="Link to this heading">#</a></h2>
<p>PETSc allows users to save/load <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code>s representing meshes,
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>s representing data layouts on the meshes, and
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code>s defined on the data layouts to/from an HDF5 file in
parallel, where one can use different number of processes for saving
and for loading.</p>
<section id="saving">
<h3>Saving<a class="headerlink" href="#saving" title="Link to this heading">#</a></h3>
<p>The simplest way to save <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> data is to use options for configuration.
This requires only the code</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DMViewFromOptions.html">DMViewFromOptions</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="s">"-dm_view"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Vec/VecViewFromOptions.html">VecViewFromOptions</a></span><span class="p">(</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="s">"-vec_view"</span><span class="p">)</span>
</pre></div>
</div>
<p>along with the command line options</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span>./myprog<span class="w"> </span>-dm_view<span class="w"> </span>hdf5:myprog.h5<span class="w"> </span>-vec_view<span class="w"> </span>hdf5:myprog.h5::append
</pre></div>
</div>
<p>Options prefixes can be used to separately control the saving and loading of various fields.
However, the user can have finer grained control by explicitly creating the PETSc objects involved.
To save data to “example.h5” file, we can first create a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a></span></code> of type <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PETSCVIEWERHDF5.html">PETSCVIEWERHDF5</a></span></code> in <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PetscFileMode.html">FILE_MODE_WRITE</a></span></code> mode as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a></span><span class="w"> </span><span class="n">viewer</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerHDF5Open.html">PetscViewerHDF5Open</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_WORLD.html">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="w"> </span><span class="s">"example.h5"</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscFileMode.html">FILE_MODE_WRITE</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>As <code class="docutils notranslate"><span class="pre">dm</span></code> is a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> object representing a mesh, we first give it a <em>mesh name</em>, “plexA”, and save it as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="s">"plexA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPushFormat.html">PetscViewerPushFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Viewer/PetscViewerFormat.html">PETSC_VIEWER_HDF5_PETSC</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMView.html">DMView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPopFormat.html">PetscViewerPopFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>The <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMView.html">DMView</a>()</span></code> call is shorthand for the following sequence</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexTopologyView.html">DMPlexTopologyView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexCoordinatesView.html">DMPlexCoordinatesView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexLabelsView.html">DMPlexLabelsView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>If the <em>mesh name</em> is not explicitly set, the default name is used.
In the above <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewerFormat.html">PETSC_VIEWER_HDF5_PETSC</a></span></code> format was used to save the entire representation of the mesh.
This format also saves global point numbers attached to the mesh points.
In this example the set of all global point numbers is <span class="math">\(X = [0, 11)\)</span>.</p>
<p>The data layout, <code class="docutils notranslate"><span class="pre">s</span></code>, needs to be wrapped in a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> object for it to be saved.
Here, we create the wrapping <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>, <code class="docutils notranslate"><span class="pre">sdm</span></code>, with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMClone.html">DMClone</a>()</span></code>, give it a <em>dm name</em>, “dmA”, attach <code class="docutils notranslate"><span class="pre">s</span></code> to <code class="docutils notranslate"><span class="pre">sdm</span></code>, and save it as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DMClone.html">DMClone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">sdm</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="s">"dmA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMSetLocalSection.html">DMSetLocalSection</a></span><span class="p">(</span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSectionView.html">DMPlexSectionView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n">sdm</span><span class="p">);</span>
</pre></div>
</div>
<p>If the <em>dm name</em> is not explicitly set, the default name is to be used.
In the above, instead of using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMClone.html">DMClone</a>()</span></code>, one could also create a new <code class="docutils notranslate"><span class="pre">DMSHELL</span></code> object to attach <code class="docutils notranslate"><span class="pre">s</span></code> to.
The first argument of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSectionView.html">DMPlexSectionView</a>()</span></code> is a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> object that represents the mesh, and the third argument is a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> object that carries the data layout that we would like to save.
They are, in general, two different objects, and the former carries a <em>mesh name</em>, while the latter carries a <em>dm name</em>.
These names are used to construct a group structure in the HDF5 file.
Note that the data layout points are associated with the mesh points, so each of them can also be tagged with a global point number in <span class="math">\(X\)</span>; <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSectionView.html">DMPlexSectionView</a>()</span></code> saves these tags along with the data layout itself, so that, when the mesh and the data layout are loaded separately later, one can associate the points in the former with those in the latter by comparing their global point numbers.</p>
<p>We now create a local vector associated with <code class="docutils notranslate"><span class="pre">sdm</span></code>, e.g., as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DM/DMGetLocalVector.html">DMGetLocalVector</a></span><span class="p">(</span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">vec</span><span class="p">);</span>
</pre></div>
</div>
<p>After setting values of <code class="docutils notranslate"><span class="pre">vec</span></code>, we name it “vecA” and save it as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="s">"vecA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexLocalVectorView.html">DMPlexLocalVectorView</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="n">vec</span><span class="p">);</span>
</pre></div>
</div>
<p>A global vector can be saved in the exact same way with trivial changes.</p>
<p>After saving, we destroy the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a></span></code> with:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Viewer/PetscViewerDestroy.html">PetscViewerDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>The output file “example.h5” now looks like the following:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">$</span><span class="w"> </span><span class="n">h5dump</span><span class="w"> </span><span class="o">--</span><span class="n">contents</span><span class="w"> </span><span class="n">example</span><span class="p">.</span><span class="n">h5</span>
<span class="n">HDF5</span><span class="w"> </span><span class="s">"example.h5"</span><span class="w"> </span><span class="p">{</span>
<span class="n">FILE_CONTENTS</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">order</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">section</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">section</span><span class="o">/</span><span class="n">atlasDof</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">section</span><span class="o">/</span><span class="n">atlasOff</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">vecs</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">vecs</span><span class="o">/</span><span class="n">vecA</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">dms</span><span class="o">/</span><span class="n">dmA</span><span class="o">/</span><span class="n">vecs</span><span class="o">/</span><span class="n">vecA</span><span class="o">/</span><span class="n">vecA</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">labels</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">cells</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">cones</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">order</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">orientation</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
</pre></div>
</div>
</section>
<section id="saving-in-the-new-parallel-hdf5-format">
<h3>Saving in the new parallel HDF5 format<a class="headerlink" href="#saving-in-the-new-parallel-hdf5-format" title="Link to this heading">#</a></h3>
<p>Since PETSc 3.19, we offer a new format which supports parallel loading.
To write in this format, you currently need to specify it explicitly using the option</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">dm_plex_view_hdf5_storage_version</span><span class="w"> </span><span class="mf">3.0.0</span>
</pre></div>
</div>
<p>The storage version is stored in the file and set automatically when loading (described below).
You can check the storage version of the HDF5 file with</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">$</span><span class="w"> </span><span class="n">h5dump</span><span class="w"> </span><span class="o">-</span><span class="n">a</span><span class="w"> </span><span class="o">/</span><span class="n">dmplex_storage_version</span><span class="w"> </span><span class="n">example</span><span class="p">.</span><span class="n">h5</span>
</pre></div>
</div>
<p>To allow for simple and efficient implementation, and good load balancing, the 3.0.0 format changes the way the mesh topology is stored.
Different strata (sets of mesh entities with an equal dimension; or vertices, edges, faces, and cells) are now stored separately.
The new structure of <code class="docutils notranslate"><span class="pre">/topologies/<mesh_name>/topology</span></code> is following:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">$</span><span class="w"> </span><span class="n">h5dump</span><span class="w"> </span><span class="o">--</span><span class="n">contents</span><span class="w"> </span><span class="n">example</span><span class="p">.</span><span class="n">h5</span>
<span class="n">HDF5</span><span class="w"> </span><span class="s">"example.h5"</span><span class="w"> </span><span class="p">{</span>
<span class="n">FILE_CONTENTS</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="p">...</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">permutation</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">0</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">0</span><span class="o">/</span><span class="n">cone_sizes</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">0</span><span class="o">/</span><span class="n">cones</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">0</span><span class="o">/</span><span class="n">orientations</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">1</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">1</span><span class="o">/</span><span class="n">cone_sizes</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">1</span><span class="o">/</span><span class="n">cones</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">1</span><span class="o">/</span><span class="n">orientations</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">2</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="n">cone_sizes</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="n">cones</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">2</span><span class="o">/</span><span class="n">orientations</span>
<span class="w"> </span><span class="n">group</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">3</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">3</span><span class="o">/</span><span class="n">cone_sizes</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">3</span><span class="o">/</span><span class="n">cones</span>
<span class="w"> </span><span class="n">dataset</span><span class="w"> </span><span class="o">/</span><span class="n">topologies</span><span class="o">/</span><span class="n">plexA</span><span class="o">/</span><span class="n">topology</span><span class="o">/</span><span class="n">strata</span><span class="o">/</span><span class="mi">3</span><span class="o">/</span><span class="n">orientations</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
</pre></div>
</div>
<p>Group <code class="docutils notranslate"><span class="pre">/topologies/<mesh_name>/topology/strata</span></code> contains a subgroup for each stratum depth (dimension; 0 for vertices up to 3 for cells).
DAG points (mesh entities) have an implicit global numbering, given by the position in <code class="docutils notranslate"><span class="pre">orientations</span></code> (or <code class="docutils notranslate"><span class="pre">cone_sizes</span></code>) plus the stratum offset.
The stratum offset is given by a sum of lengths of all previous strata with respect to the order stored in <code class="docutils notranslate"><span class="pre">/topologies/<mesh_name>/topology/permutation</span></code>.
This global numbering is compatible with the explicit numbering in dataset <code class="docutils notranslate"><span class="pre">topology/order</span></code> of previous versions.</p>
<p>For a DAG point with index <code class="docutils notranslate"><span class="pre">i</span></code> at depth <code class="docutils notranslate"><span class="pre">s</span></code>, <code class="docutils notranslate"><span class="pre">cone_sizes[i]</span></code> gives a size of this point’s cone (set of adjacent entities with depth <code class="docutils notranslate"><span class="pre">s-1</span></code>).
Let <code class="docutils notranslate"><span class="pre">o</span> <span class="pre">=</span> <span class="pre">sum(cone_sizes[0:i]])</span></code> (in Python syntax).
Points forming the cone are then given by <code class="docutils notranslate"><span class="pre">cones[o:o+cone_sizes[i]]</span></code> (in numbering relative to the depth <code class="docutils notranslate"><span class="pre">s-1</span></code>).
The orientation of the cone with respect to point <code class="docutils notranslate"><span class="pre">i</span></code> is then stored in <code class="docutils notranslate"><span class="pre">orientations[i]</span></code>.</p>
</section>
<section id="loading">
<h3>Loading<a class="headerlink" href="#loading" title="Link to this heading">#</a></h3>
<p>To load data from “example.h5” file, we create a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a></span></code>
of type <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PETSCVIEWERHDF5.html">PETSCVIEWERHDF5</a></span></code> in <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PetscFileMode.html">FILE_MODE_READ</a></span></code> mode as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Viewer/PetscViewerHDF5Open.html">PetscViewerHDF5Open</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_WORLD.html">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="w"> </span><span class="s">"example.h5"</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscFileMode.html">FILE_MODE_READ</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>We then create a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> object, give it a <em>mesh name</em>, “plexA”, and load
the mesh as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DMCreate.html">DMCreate</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_WORLD.html">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">dm</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMSetType.html">DMSetType</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="s">"plexA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPushFormat.html">PetscViewerPushFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Viewer/PetscViewerFormat.html">PETSC_VIEWER_HDF5_PETSC</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMLoad.html">DMLoad</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPopFormat.html">PetscViewerPopFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>where <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewerFormat.html">PETSC_VIEWER_HDF5_PETSC</a></span></code> format was again used. The user can have more control by replace the single load call with</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span><span class="w"> </span><span class="n">sfO</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DM/DMCreate.html">DMCreate</a></span><span class="p">(</span><span class="n"><a href="../manualpages/Sys/PETSC_COMM_WORLD.html">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">dm</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DM/DMSetType.html">DMSetType</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="s">"plexA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPushFormat.html">PetscViewerPushFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Viewer/PetscViewerFormat.html">PETSC_VIEWER_HDF5_PETSC</a></span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexTopologyLoad.html">DMPlexTopologyLoad</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">sfO</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexCoordinatesLoad.html">DMPlexCoordinatesLoad</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n">sfO</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Viewer/PetscViewerPopFormat.html">PetscViewerPopFormat</a></span><span class="p">(</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>The object returned by <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexTopologyLoad.html">DMPlexTopologyLoad</a>()</span></code>, <code class="docutils notranslate"><span class="pre">sfO</span></code>, is a
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> that pushes forward <span class="math">\(X\)</span> to the loaded mesh,
<code class="docutils notranslate"><span class="pre">dm</span></code>; this <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> is constructed with the global point
number tags that we saved along with the mesh points.</p>
<p>As the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> mesh just loaded might not have a desired distribution,
it is common to redistribute the mesh for a better distribution using
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexDistribute.html">DMPlexDistribute</a>()</span></code>, e.g., as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">distributedDM</span><span class="p">;</span>
<span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">overlap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<span class="n"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span><span class="w"> </span><span class="n">sfDist</span><span class="p">,</span><span class="w"> </span><span class="n">sf</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexDistribute.html">DMPlexDistribute</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">overlap</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">sfDist</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">distributedDM</span><span class="p">);</span>
<span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">distributedDM</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../manualpages/DM/DMDestroy.html">DMDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">dm</span><span class="p">);</span>
<span class="w"> </span><span class="n">dm</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">distributedDM</span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="s">"plexA"</span><span class="p">);</span>
<span class="p">}</span>
<span class="n"><a href="../manualpages/PetscSF/PetscSFCompose.html">PetscSFCompose</a></span><span class="p">(</span><span class="n">sfO</span><span class="p">,</span><span class="w"> </span><span class="n">sfDist</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">sf</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSF/PetscSFDestroy.html">PetscSFDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">sfO</span><span class="p">);</span>
<span class="n"><a href="../manualpages/PetscSF/PetscSFDestroy.html">PetscSFDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">sfDist</span><span class="p">);</span>
</pre></div>
</div>
<p>Note that the new <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> does not automatically inherit the <em>mesh name</em>,
so we need to name it “plexA” once again. <code class="docutils notranslate"><span class="pre">sfDist</span></code> is a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code>
that pushes forward the loaded mesh to the redistributed mesh, so, composed
with <code class="docutils notranslate"><span class="pre">sfO</span></code>, it makes the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> that pushes forward <span class="math">\(X\)</span>
directly to the redistributed mesh, which we call <code class="docutils notranslate"><span class="pre">sf</span></code>.</p>
<p>We then create a new <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>, <code class="docutils notranslate"><span class="pre">sdm</span></code>, with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMClone.html">DMClone</a>()</span></code>, give it
a <em>dm name</em>, “dmA”, and load the on-disk data layout into <code class="docutils notranslate"><span class="pre">sdm</span></code> as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span><span class="w"> </span><span class="n">globalDataSF</span><span class="p">,</span><span class="w"> </span><span class="n">localDataSF</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DM/DMClone.html">DMClone</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">sdm</span><span class="p">);</span>
<span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="s">"dmA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexSectionLoad.html">DMPlexSectionLoad</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="n">sf</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">globalDataSF</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">localDataSF</span><span class="p">);</span>
</pre></div>
</div>
<p>where we could also create a new
<code class="docutils notranslate"><span class="pre">DMSHELL</span></code> object instead of using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMClone.html">DMClone</a>()</span></code>.
Each point in the on-disk data layout being tagged with a global
point number in <span class="math">\(X\)</span>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSectionLoad.html">DMPlexSectionLoad</a>()</span></code>
internally constructs a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> that pushes forward the on-disk
data layout to <span class="math">\(X\)</span>.
Composing this with <code class="docutils notranslate"><span class="pre">sf</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPlexSectionLoad.html">DMPlexSectionLoad</a>()</span></code> internally
constructs another <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> that pushes forward the on-disk
data layout directly to the redistributed mesh. It then
reconstructs the data layout <code class="docutils notranslate"><span class="pre">s</span></code> on the redistributed mesh and
attaches it to <code class="docutils notranslate"><span class="pre">sdm</span></code>. The objects returned by this function,
<code class="docutils notranslate"><span class="pre">globalDataSF</span></code> and <code class="docutils notranslate"><span class="pre">localDataSF</span></code>, are <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code>s that can
be used to migrate the on-disk vector data into local and global
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code>s defined on <code class="docutils notranslate"><span class="pre">sdm</span></code>.</p>
<p>We now create a local vector associated with <code class="docutils notranslate"><span class="pre">sdm</span></code>, e.g., as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
<span class="n"><a href="../manualpages/DM/DMGetLocalVector.html">DMGetLocalVector</a></span><span class="p">(</span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">vec</span><span class="p">);</span>
</pre></div>
</div>
<p>We then name <code class="docutils notranslate"><span class="pre">vec</span></code> “vecA” and load the on-disk vector into <code class="docutils notranslate"><span class="pre">vec</span></code> as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Sys/PetscObjectSetName.html">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="../manualpages/Sys/PetscObject.html">PetscObject</a></span><span class="p">)</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="s">"vecA"</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexLocalVectorLoad.html">DMPlexLocalVectorLoad</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">viewer</span><span class="p">,</span><span class="w"> </span><span class="n">sdm</span><span class="p">,</span><span class="w"> </span><span class="n">localDataSF</span><span class="p">,</span><span class="w"> </span><span class="n">localVec</span><span class="p">);</span>
</pre></div>
</div>
<p>where <code class="docutils notranslate"><span class="pre">localDataSF</span></code> knows how to migrate the on-disk vector
data into a local <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> defined on <code class="docutils notranslate"><span class="pre">sdm</span></code>.
The on-disk vector can be loaded into a global vector associated with
<code class="docutils notranslate"><span class="pre">sdm</span></code> in the exact same way with trivial changes.</p>
<p>After loading, we destroy the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a></span></code> with:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/Viewer/PetscViewerDestroy.html">PetscViewerDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">viewer</span><span class="p">);</span>
</pre></div>
</div>
<p>The above infrastructure works seamlessly in distributed-memory parallel
settings, in which one can even use different number of processes for
saving and for loading; a more comprehensive example is found in
<a href="../src/dm/impls/plex/tutorials/ex12.c.html">DMPlex Tutorial ex12</a>.</p>
</section>
</section>
<section id="metric-based-mesh-adaptation">
<span id="dm-adaptor-table"></span><h2>Metric-based mesh adaptation<a class="headerlink" href="#metric-based-mesh-adaptation" title="Link to this heading">#</a></h2>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> supports mesh adaptation using the <em>Riemannian metric framework</em>.
The idea is to use a Riemannian metric space within the mesher. The
metric space dictates how mesh resolution should be distributed across
the domain. Using this information, the remesher transforms the mesh such
that it is a <em>unit mesh</em> when viewed in the metric space. That is, the image
of each of its elements under the mapping from Euclidean space into the
metric space has edges of unit length.</p>
<p>One of the main advantages of metric-based mesh adaptation is that it allows
for fully anisotropic remeshing. That is, it provides a means of controlling
the shape and orientation of elements in the adapted mesh, as well as their
size. This can be particularly useful for advection-dominated and
directionally-dependent problems.</p>
<p>See <span id="id2">[<a class="reference internal" href="#id3895" title="Frédéric Alauzet. Metric-based anisotropic mesh adaptation. https://pages.saclay.inria.fr/frederic.alauzet/cours/cea2010_V3.pdf, 2010.">Ala10</a>]</span> for further details on metric-based anisotropic mesh
adaptation.</p>
<p>The two main ingredients for metric-based mesh adaptation are an input mesh
(i.e. the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code>) and a Riemannian metric. The implementation in PETSc assumes
that the metric is piecewise linear and continuous across elemental boundaries.
Such an object can be created using the routine</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricCreate.html">DMPlexMetricCreate</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">field</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="o">*</span><span class="n">metric</span><span class="p">);</span>
</pre></div>
</div>
<p>A metric must be symmetric positive-definite, so that distances may be properly
defined. This can be checked using</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricEnforceSPD.html">DMPlexMetricEnforceSPD</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricIn</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscBool.html">PetscBool</a></span><span class="w"> </span><span class="n">restrictSizes</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscBool.html">PetscBool</a></span><span class="w"> </span><span class="n">restrictAnisotropy</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricOut</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">determinant</span><span class="p">);</span>
</pre></div>
</div>
<p>This routine may also be used to enforce minimum and maximum tolerated metric
magnitudes (i.e. cell sizes), as well as maximum anisotropy. These quantities
can be specified using</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricSetMinimumMagnitude.html">DMPlexMetricSetMinimumMagnitude</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">h_min</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexMetricSetMaximumMagnitude.html">DMPlexMetricSetMaximumMagnitude</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">h_max</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexMetricSetMaximumAnisotropy.html">DMPlexMetricSetMaximumAnisotropy</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">a_max</span><span class="p">);</span>
</pre></div>
</div>
<p>or the command line arguments</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">dm_plex_metric_h_min</span><span class="w"> </span><span class="o"><</span><span class="n">h_min</span><span class="o">></span>
<span class="o">-</span><span class="n">dm_plex_metric_h_max</span><span class="w"> </span><span class="o"><</span><span class="n">h_max</span><span class="o">></span>
<span class="o">-</span><span class="n">dm_plex_metric_a_max</span><span class="w"> </span><span class="o"><</span><span class="n">a_max</span><span class="o">></span>
</pre></div>
</div>
<p>One simple way to combine two metrics is by simply averaging them entry-by-entry.
Another is to <em>intersect</em> them, which amounts to choosing the greatest level of
refinement in each direction. These operations are available in PETSc through
the routines</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricAverage.html">DMPlexMetricAverage</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">numMetrics</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">weights</span><span class="p">[],</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metrics</span><span class="p">[],</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricAvg</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexMetricIntersection.html">DMPlexMetricIntersection</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="n">numMetrics</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metrics</span><span class="p">[],</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricInt</span><span class="p">);</span>
</pre></div>
</div>
<p>However, before combining metrics, it is important that they are scaled in the same
way. Scaling also allows the user to control the number of vertices in the adapted
mesh (in an approximate sense). This is achieved using the <span class="math">\(L^p\)</span> normalization
framework, with the routine</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricNormalize.html">DMPlexMetricNormalize</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricIn</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscBool.html">PetscBool</a></span><span class="w"> </span><span class="n">restrictSizes</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscBool.html">PetscBool</a></span><span class="w"> </span><span class="n">restrictAnisotropy</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metricOut</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">determinant</span><span class="p">);</span>
</pre></div>
</div>
<p>There are two important parameters for the normalization: the normalization order
<span class="math">\(p\)</span> and the target metric complexity, which is analogous to the vertex count.
They are controlled using</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMPlex/DMPlexMetricSetNormalizationOrder.html">DMPlexMetricSetNormalizationOrder</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
<span class="n"><a href="../manualpages/DMPlex/DMPlexMetricSetTargetComplexity.html">DMPlexMetricSetTargetComplexity</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscReal.html">PetscReal</a></span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
</pre></div>
</div>
<p>or the command line arguments</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">-dm_plex_metric_p <p></span>
<span class="go">-dm_plex_metric_target_complexity <target></span>
</pre></div>
</div>
<p>Two different metric-based mesh adaptation tools are available in PETSc:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://meshadaptation.github.io/">Pragmatic</a>;</p></li>
<li><p><a class="reference external" href="https://www.mmgtools.org/">Mmg/ParMmg</a>.</p></li>
</ul>
<p>Mmg is a serial package, whereas ParMmg is the MPI version.
Note that surface meshing is not currently supported and that ParMmg
works only in three dimensions. Mmg can be used for both two and three dimensional problems.
Pragmatic, Mmg and ParMmg may be specified by the command line arguments</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">dm_adaptor</span><span class="w"> </span><span class="n">pragmatic</span>
<span class="o">-</span><span class="n">dm_adaptor</span><span class="w"> </span><span class="n">mmg</span>
<span class="o">-</span><span class="n">dm_adaptor</span><span class="w"> </span><span class="n">parmmg</span>
</pre></div>
</div>
<p>Once a metric has been constructed, it can be used to perform metric-based
mesh adaptation using the routine</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DM/DMAdaptMetric.html">DMAdaptMetric</a></span><span class="p">(</span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Vec/Vec.html">Vec</a></span><span class="w"> </span><span class="n">metric</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/DM/DMLabel.html">DMLabel</a></span><span class="w"> </span><span class="n">bdLabel</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/DM/DMLabel.html">DMLabel</a></span><span class="w"> </span><span class="n">rgLabel</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/DM/DM.html">DM</a></span><span class="w"> </span><span class="n">dmAdapt</span><span class="p">);</span>
</pre></div>
</div>
<p>where <code class="docutils notranslate"><span class="pre">bdLabel</span></code> and <code class="docutils notranslate"><span class="pre">rgLabel</span></code> are boundary and interior tags to be
preserved under adaptation, respectively.</p>
<p class="rubric">Footnotes</p>
<div class="docutils container" id="id1">
<div role="list" class="citation-list">
<div class="citation" id="id3895" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">Ala10</a><span class="fn-bracket">]</span></span>
<p>Frédéric Alauzet. Metric-based anisotropic mesh adaptation. <a class="reference external" href="https://pages.saclay.inria.fr/frederic.alauzet/cours/cea2010_V3.pdf">https://pages.saclay.inria.fr/frederic.alauzet/cours/cea2010_V3.pdf</a>, 2010.</p>
</div>
</div>
</div>
</section>
</section>
<hr class="footnotes docutils" />
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="boundary-footnote" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>In three dimensions, the boundary of a cell (sometimes called an element) is its faces, the boundary of a face is its edges and the boundary of an edge is the two vertices.</p>
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