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<section class="tex2jax_ignore mathjax_ignore" id="petscsection-connecting-grids-to-data">
<span id="ch-petscsection"></span><h1>PetscSection: Connecting Grids to Data<a class="headerlink" href="#petscsection-connecting-grids-to-data" title="Link to this heading">#</a></h1>
<p>The strongest links between solvers and discretizations are</p>
<ul class="simple">
<li><p>the relationship between the layout of data over a mesh (or similar structure) and the data layout in arrays and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> used for computation,</p></li>
<li><p>data partitioning, and</p></li>
<li><p>ordering of data.</p></li>
</ul>
<p>To enable modularity, we encode the operations above in simple data
structures that can be understood by the linear algebraic and solver components of PETSc (<code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/Mat.html">Mat</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSP.html">KSP</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PC.html">PC</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/SNES/SNES.html">SNES</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/TS/TS.html">TS</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Tao/Tao.html">Tao</a></span></code>)
without explicit reference to the mesh (topology) or discretization (analysis).</p>
<p>While <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is currently only employed for <code class="docutils notranslate"><span class="pre">DMPlex</span></code>, <code class="docutils notranslate"><span class="pre">DMForest</span></code>, and <code class="docutils notranslate"><span class="pre">DMNetwork</span></code> mesh descriptions, much of its operation is general enough to be utilized for other types of discretizations.
This section will explain the basic concepts of a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> that are generalizable to other mesh descriptions.</p>
<section id="general-concept">
<span id="sec-petscsection-concept"></span><h2>General concept<a class="headerlink" href="#general-concept" title="Link to this heading">#</a></h2>
<p>Specific entries (or collections of entries) in a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> (or a simple array) can be associated with a “location” on a mesh (or other types of data structure) using the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> object.
A <strong>point</strong> is a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span></code> that serves as an abstract “index” into arrays from iterable sets, such as k-cells in a mesh.
Other iterable set examples can be as simple as the points of a finite difference grid, or cells of a finite volume grid, or as complex as the topological entities of an unstructured mesh (cells, faces, edges, and vertices).</p>
<p>At it’s most basic, a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is a mapping between the mesh points and a tuple <code class="docutils notranslate"><span class="pre">(ndof,</span> <span class="pre">offset)</span></code>, where <code class="docutils notranslate"><span class="pre">ndof</span></code> is the number of values stored at that mesh point and <code class="docutils notranslate"><span class="pre">offset</span></code> is the location in the array of that data.
So given the tuple for a mesh point, its data can be accessed by <code class="docutils notranslate"><span class="pre">array[offset</span> <span class="pre">+</span> <span class="pre">d]</span></code>, where <code class="docutils notranslate"><span class="pre">d</span></code> in <code class="docutils notranslate"><span class="pre">[0,</span> <span class="pre">ndof)</span></code> is the dof to access.</p>
<section id="charts-defining-mesh-points">
<h3>Charts: Defining mesh points<a class="headerlink" href="#charts-defining-mesh-points" title="Link to this heading">#</a></h3>
<p>The mesh points for a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> must be contiguously numbered and are defined to be in some range <span class="math">\([\mathrm{pStart}, \mathrm{pEnd})\)</span>, which is called a <strong>chart</strong>.
The chart of a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is set via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetChart.html">PetscSectionSetChart</a>()</span></code>.
Note that even though the mesh points must be contiguously numbered, the indexes into the array (defined by each <code class="docutils notranslate"><span class="pre">(ndof,</span> <span class="pre">offset)</span></code> tuple) associated with the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> need not be.
In other words, there may be elements in the array that are not associated with any mesh points, though this is not often the case.</p>
</section>
<section id="defining-the-ndof-offset-tuple">
<h3>Defining the (ndof, offset) tuple<a class="headerlink" href="#defining-the-ndof-offset-tuple" title="Link to this heading">#</a></h3>
<p>Defining the <code class="docutils notranslate"><span class="pre">(ndof,</span> <span class="pre">offset)</span></code> tuple for each mesh point generally first starts with setting the <code class="docutils notranslate"><span class="pre">ndof</span></code> for each point, which is done using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a>()</span></code>.
This associates a set of degrees of freedom (dof), (a small space <span class="math">\(\{e_k\}\ 0 < k < ndof\)</span>), with every point.
If <code class="docutils notranslate"><span class="pre">ndof</span></code> is not set for a mesh point, it is assumed to be 0.</p>
<p>The offset for each mesh point is usually set automatically by <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code>.
This will concatenate each mesh point’s dofs together in the order of the mesh points.
This concatenation can be done in a different order by setting a permutation, which is described in <a class="reference internal" href="#sec-petscsection-permutation"><span class="std std-ref">Permutation: Changing the order of array data</span></a>.</p>
<p>Alternatively, the offset for each mesh point can be set manually by <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetOffset.html">PetscSectionSetOffset</a>()</span></code>, though this is not commonly needed.</p>
<p>Once the tuples are created, the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is ready to use.</p>
</section>
<section id="basic-setup-example">
<h3>Basic Setup Example<a class="headerlink" href="#basic-setup-example" title="Link to this heading">#</a></h3>
<p>To summarize, the sequence for constructing a basic <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is the following:</p>
<ol class="arabic simple">
<li><p>Specify the range of points, or chart, with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetChart.html">PetscSectionSetChart</a>()</span></code>.</p></li>
<li><p>Specify the number of dofs per point with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a>()</span></code>. Any values not set will be zero.</p></li>
<li><p>Set up the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code>.</p></li>
</ol>
</section>
</section>
<section id="multiple-fields">
<h2>Multiple Fields<a class="headerlink" href="#multiple-fields" title="Link to this heading">#</a></h2>
<p>In many discretizations, it is useful to differentiate between different kinds of dofs present on a mesh.
For example, a dof attached to a cell point might represent pressure while dofs on vertices might represent velocity or displacement.
A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> can represent this additional structure with what are called <strong>fields</strong>.
<strong>Fields</strong> are indexed contiguously from <code class="docutils notranslate"><span class="pre">[0,</span> <span class="pre">num_fields)</span></code>.
To set the number of fields for a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>, call <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetNumFields.html">PetscSectionSetNumFields</a>()</span></code>.</p>
<p>Internally, each field is stored in a separate <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>.
In fact, all the concepts and functions presented in <a class="reference internal" href="#sec-petscsection-concept"><span class="std std-ref">General concept</span></a> were actually applied onto the <strong>default field</strong>, which is indexed as <code class="docutils notranslate"><span class="pre">0</span></code>.
The fields inherit the same chart as the “parent” <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>.</p>
<section id="setting-up-multiple-fields">
<h3>Setting Up Multiple Fields<a class="headerlink" href="#setting-up-multiple-fields" title="Link to this heading">#</a></h3>
<p>Setup for a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with multiple fields is nearly identical to setup for a single field.</p>
<p>The sequence for constructing such a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> is the following:</p>
<ol class="arabic simple">
<li><p>Specify the range of points, or chart, with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetChart.html">PetscSectionSetChart</a>()</span></code>. All fields share the same chart.</p></li>
<li><p>Specify the number of fields with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetNumFields.html">PetscSectionSetNumFields</a>()</span></code>.</p></li>
<li><p>Set the number of dof for each point on each field with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetFieldDof.html">PetscSectionSetFieldDof</a>()</span></code>. Any values not set will be zero.</p></li>
<li><p>Set the <strong>total</strong> number of dof for each point with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetDof.html">PetscSectionSetDof</a>()</span></code>. Thus value must be greater than or equal to the sum of the values set with
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetFieldDof.html">PetscSectionSetFieldDof</a>()</span></code> at that point. Again, values not set will be zero.</p></li>
<li><p>Set up the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code>.</p></li>
</ol>
</section>
<section id="point-major-or-field-major">
<h3>Point Major or Field Major<a class="headerlink" href="#point-major-or-field-major" title="Link to this heading">#</a></h3>
<p>A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with one field and and offsets set in <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code> may be thought of as defining a two dimensional array indexed by point in the outer dimension with a variable length inner dimension indexed by the dof at that point: <span class="math">\(v[\mathrm{pStart} <= point < \mathrm{pEnd}][0 <= dof < \mathrm{ndof}]\)</span> <a class="footnote-reference brackets" href="#petscsection-footnote" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
<p>With multiple fields, this array is now three dimensional, with the outer dimensions being both indexed by mesh points and field points.
Thus, there is a choice on whether to index by points first, or by fields first.
In other words, will the array be laid out in a point-major or field-major fashion.</p>
<p>Point-major ordering corresponds to <span class="math">\(v[\mathrm{pStart} <= point < \mathrm{pEnd}][0 <= field < \mathrm{num\_fields}][0 <= dof < \mathrm{ndof}]\)</span>.
All the dofs for each mesh point are stored contiguously, meaning the fields are <strong>interlaced</strong>.
Field-major ordering corresponds to <span class="math">\(v[0 <= field < \mathrm{num\_fields}][\mathrm{pStart} <= point < \mathrm{pEnd}][0 <= dof < \mathrm{ndof}]\)</span>.
The all the dofs for each field are stored contiguously, meaning the points are <strong>interlaced</strong>.</p>
<p>Consider a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with 2 fields and 2 points (from 0 to 2). Let the 0th field have <code class="docutils notranslate"><span class="pre">ndof=1</span></code> for each point and the 1st field have <code class="docutils notranslate"><span class="pre">ndof=2</span></code> for each point.
Denote each array entry <span class="math">\((p_i, f_i, d_i)\)</span> for <span class="math">\(p_i\)</span> being the ith point, <span class="math">\(f_i\)</span> being the ith field, and <span class="math">\(d_i\)</span> being the ith dof.</p>
<p>Point-major order would result in:</p>
<div class="math">
\[
[(p_0, f_0, d_0), (p_0, f_1, d_0), (p_0, f_1, d_1),\\ (p_1, f_0, d_0), (p_1, f_1, d_0), (p_1, f_1, d_1)]
\]</div>
<p>Conversely, field-major ordering would result in:</p>
<div class="math">
\[
[(p_0, f_0, d_0), (p_1, f_0, d_0),\\ (p_0, f_1, d_0), (p_0, f_1, d_1), (p_1, f_1, d_0), (p_1, f_1, d_1)]
\]</div>
<p>Note that dofs are always contiguous, regardless of the outer dimensional ordering.</p>
<p>Setting the which ordering is done with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetPointMajor.html">PetscSectionSetPointMajor</a>()</span></code>, where <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PETSC_TRUE.html">PETSC_TRUE</a></span></code> sets point-major and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PETSC_FALSE.html">PETSC_FALSE</a></span></code> sets field major.</p>
<p><strong>NOTE:</strong> The current default is for point-major, and many operations on <code class="docutils notranslate"><span class="pre">DMPlex</span></code> will only work with this ordering. Field-major ordering is provided mainly for compatibility with external packages, such as LibMesh.</p>
</section>
</section>
<section id="working-with-data">
<h2>Working with data<a class="headerlink" href="#working-with-data" title="Link to this heading">#</a></h2>
<p>Once a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> has been created one can use <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionGetStorageSize.html">PetscSectionGetStorageSize</a>()</span></code> to determine the total number of entries that can be stored in an array or <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> accessible by the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>.
This is most often used when creating a new <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> for a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> such as:</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>The memory locations in the associated array are found using an <strong>offset</strong> which can be obtained with:</p>
<p>Single-field <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/PetscSection/PetscSectionGetOffset.html">PetscSectionGetOffset</a></span><span class="p">(</span><span class="n"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></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">point</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="o">&</span><span class="n">offset</span><span class="p">);</span>
</pre></div>
</div>
<p>Multi-field <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code>:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/PetscSection/PetscSectionGetFieldOffset.html">PetscSectionGetFieldOffset</a></span><span class="p">(</span><span class="n"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></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">point</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/Sys/PetscInt.html">PetscInt</a></span><span class="w"> </span><span class="o">&</span><span class="n">offset</span><span class="p">);</span>
</pre></div>
</div>
<p>The value in the array is then accessed with <code class="docutils notranslate"><span class="pre">array[offset</span> <span class="pre">+</span> <span class="pre">d]</span></code>, where <code class="docutils notranslate"><span class="pre">d</span></code> in <code class="docutils notranslate"><span class="pre">[0,</span> <span class="pre">ndof)</span></code> is the dof to access.</p>
</section>
<section id="global-sections-constrained-and-distributed-data">
<h2>Global Sections: Constrained and Distributed Data<a class="headerlink" href="#global-sections-constrained-and-distributed-data" title="Link to this heading">#</a></h2>
<p>To handle distributed data and data with constraints, we use a pair of <code class="docutils notranslate"><span class="pre">PetscSections</span></code> called the <code class="docutils notranslate"><span class="pre">localSection</span></code> and <code class="docutils notranslate"><span class="pre">globalSection</span></code>.
Their use for each is described below.</p>
<section id="distributed-data">
<h3>Distributed Data<a class="headerlink" href="#distributed-data" title="Link to this heading">#</a></h3>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> can also be applied to distributed problems as well.
This is done using the same local/global system described in <a class="reference internal" href="vec.html#sec-localglobal"><span class="std std-ref">Local/global vectors and communicating between vectors</span></a>.
To do this, we introduce three new concepts; a <code class="docutils notranslate"><span class="pre">localSection</span></code>, <code class="docutils notranslate"><span class="pre">globalSection</span></code>, <code class="docutils notranslate"><span class="pre">pointSF</span></code>, and <code class="docutils notranslate"><span class="pre">sectionSF</span></code>.</p>
<p>Assume the mesh points of the “global” mesh are partitioned amongst processes and that some mesh points are shared between multiple processes (i.e there is an overlap in the partitions).
The shared mesh points define the ghost/halo points needed in many PDE problems.
For each shared mesh point, appoint one process to be the owner of that mesh point.
To describe this parallel mesh point layout, we use a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> and call it the <code class="docutils notranslate"><span class="pre">pointSF</span></code>.
The <code class="docutils notranslate"><span class="pre">pointSF</span></code> describes which processes “own” which mesh points and which process is the owner of each shared mesh point.</p>
<p>Next, for each process define a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> that describes the mapping between that process’s partition (including shared mesh points) and the data stored on it and call it the <code class="docutils notranslate"><span class="pre">localSection</span></code>.
The <code class="docutils notranslate"><span class="pre">localSection</span></code> describes the layout of the local vector.
To generate the <code class="docutils notranslate"><span class="pre">globalSection</span></code> we use <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionCreateGlobalSection.html">PetscSectionCreateGlobalSection</a>()</span></code>, which takes the <code class="docutils notranslate"><span class="pre">localSection</span></code> and <code class="docutils notranslate"><span class="pre">pointSF</span></code> as inputs.
The global section returns <span class="math">\(-(dof+1)\)</span> for the number of dofs on an unowned (ghost) point, and traditionally <span class="math">\(-(off+1)\)</span> for its offset on the owning process.
This behavior of the offsets is controlled via an argument to <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionCreateGlobalSection.html">PetscSectionCreateGlobalSection</a>()</span></code>.
The <code class="docutils notranslate"><span class="pre">globalSection</span></code> can be used to create global vectors, just as the local section is used to create local vectors.</p>
<p>To perform the global-to-local and local-to-global communication, we define <code class="docutils notranslate"><span class="pre">sectionSF</span></code> to be the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> describing the mapping between the local and global vectors.
This is generated via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSFSetGraphSection.html">PetscSFSetGraphSection</a>()</span></code>.
Using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSFBcastBegin.html">PetscSFBcastBegin</a>()</span></code> will send data from the global vector to the local vector, while <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSFReduceBegin.html">PetscSFReduceBegin</a>()</span></code> will send data from the local vector to the global vector.</p>
<p>If using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>, this entire process is done automatically.
The <code class="docutils notranslate"><span class="pre">localSection</span></code>, <code class="docutils notranslate"><span class="pre">globalSection</span></code>, <code class="docutils notranslate"><span class="pre">pointSF</span></code>, and <code class="docutils notranslate"><span class="pre">sectionSF</span></code> on a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> can be obtained via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetLocalSection.html">DMGetLocalSection</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetGlobalSection.html">DMGetGlobalSection</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetPointSF.html">DMGetPointSF</a>()</span></code>, and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetSectionSF.html">DMGetSectionSF</a>()</span></code>, respectively.
Additionally, communication from global to local vectors and vice versa can be done via <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGlobalToLocal.html">DMGlobalToLocal</a>()</span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMLocalToGlobal.html">DMLocalToGlobal</a>()</span></code> as described in <a class="reference internal" href="vec.html#sec-localglobal"><span class="std std-ref">Local/global vectors and communicating between vectors</span></a>.
Note that not all <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> types use this system, such as <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code> (see <a class="reference internal" href="vec.html#sec-struct"><span class="std std-ref">DMDA - Creating vectors for structured grids</span></a>).</p>
</section>
<section id="constrained-data">
<h3>Constrained Data<a class="headerlink" href="#constrained-data" title="Link to this heading">#</a></h3>
<p>In addition to describing parallel data, the <code class="docutils notranslate"><span class="pre">localSection</span></code>/<code class="docutils notranslate"><span class="pre">globalSection</span></code> pair can be used to describe <em>constrained</em> dofs
These constraints usually represent essential (Dirichlet) boundary conditions, or algebraic constraints.
They are dofs that have a given fixed value, so they are present in local vectors for finite element/volume assembly or finite difference stencil application purposes, but generally absent from global vectors since they are not unknowns in the algebraic solves.</p>
<p>Constraints should be indicated in the <code class="docutils notranslate"><span class="pre">localSection</span></code>.
Use <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetConstraintDof.html">PetscSectionSetConstraintDof</a>()</span></code> to set the number of constrained dofs for a given point, and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetConstraintIndices.html">PetscSectionSetConstraintIndices</a>()</span></code> to indicate which dofs on the given point are constrained.
This must be done before <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionCreateGlobalSection.html">PetscSectionCreateGlobalSection</a>()</span></code> is called to create the <code class="docutils notranslate"><span class="pre">globalSection</span></code>.</p>
<p>Note that it is possible to have constraints set in a <code class="docutils notranslate"><span class="pre">localSection</span></code>, but have the <code class="docutils notranslate"><span class="pre">globalSection</span></code> be generated to include those constraints.
This is useful when doing some form of post-processing of a solution where you want to access all data (see <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DMGetOutputDM.html">DMGetOutputDM</a>()</span></code> for example).
See <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionCreateGlobalSection.html">PetscSectionCreateGlobalSection</a>()</span></code> for more details on this.</p>
</section>
</section>
<section id="permutation-changing-the-order-of-array-data">
<span id="sec-petscsection-permutation"></span><h2>Permutation: Changing the order of array data<a class="headerlink" href="#permutation-changing-the-order-of-array-data" title="Link to this heading">#</a></h2>
<p>By default, when <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code> is called, the data laid out in the associated array is assumed to be in the same order of the grid points.
For example, the DoFs associated with grid point 0 appear directly before grid point 1, which appears before grid point 2, etc.</p>
<p>It may be desired to have a different the ordering of data in the array than the order of grid points defined by a section.
For example, one may want grid points associated with the boundary of a domain to appear before points associated with the interior of the domain.</p>
<p>This can be accomplished by either changing the indexes of the grid points themselves, or by informing the section of the change in array ordering.
Either method uses an <code class="docutils notranslate"><span class="pre"><a href="../manualpages/IS/IS.html">IS</a></span></code> to define the permutation.</p>
<p>To change the indices of the grid points, call <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionPermute.html">PetscSectionPermute</a>()</span></code> to generate a new <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> with the desired grid point permutation.</p>
<p>To just change the array layout without changing the grid point indexing, call <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetPermutation.html">PetscSectionSetPermutation</a>()</span></code>.
This must be called before <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSectionSetUp.html">PetscSectionSetUp</a>()</span></code> and will only affect the calculation of the offsets for each grid point.</p>
</section>
<section id="dmplex-specific-functionality-obtaining-data-from-the-array">
<h2>DMPlex Specific Functionality: Obtaining data from the array<a class="headerlink" href="#dmplex-specific-functionality-obtaining-data-from-the-array" title="Link to this heading">#</a></h2>
<p>A vanilla <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> (what’s been described up till now) gives a relatively naive perspective on the underlying data; it doesn’t describe how DoFs attached to a single grid point are ordered or how different grid points relate to each other.
A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> can store and use this extra information in the form of <strong>closures</strong>, <strong>symmetries</strong>, and <strong>closure permutations</strong>.
These features currently target <code class="docutils notranslate"><span class="pre">DMPlex</span></code> and other unstructured grid descriptions.
A description of those features will be left to <a class="reference internal" href="dmplex.html#ch-unstructured"><span class="std std-ref">DMPlex: Unstructured Grids</span></a>.</p>
<p class="rubric">Footnotes</p>
<span class="target" id="id1"></span></section>
</section>
<hr class="footnotes docutils" />
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="petscsection-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>A <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> can be thought of as a generalization of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/IS/PetscLayout.html">PetscLayout</a></span></code>, in the same way that a fiber bundle is a generalization
of the normal Euclidean basis used in linear algebra. With <code class="docutils notranslate"><span class="pre"><a href="../manualpages/IS/PetscLayout.html">PetscLayout</a></span></code>, we associate a unit vector (<span class="math">\(e_i\)</span>) with every
point in the space, and just divide up points between processes.
Conversely, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a></span></code> associates multiple unit vectors with every mesh point (one for each dof) and divides the mesh points between processes using a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PetscSF/PetscSF.html">PetscSF</a></span></code> to define the distribution.</p>
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