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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>
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<section class="tex2jax_ignore mathjax_ignore" id="dmstag-staggered-structured-grid">
<span id="ch-stag"></span><h1>DMSTAG: Staggered, Structured Grid<a class="headerlink" href="#dmstag-staggered-structured-grid" title="Link to this heading">#</a></h1>
<p>For structured (aka “regular”) grids with staggered data (living on elements, faces, edges,
and/or vertices), the <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object is available. This can
be useful for problems in many domains, including fluid flow, MHD, and seismology.</p>
<p>It is possible, though cumbersome, to implement a staggered-grid code using multiple <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code> objects, or a single multi-component <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code> object where some degrees of freedom are unused.
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> was developed for two main purposes:</p>
<ol class="arabic simple">
<li><p>To help manage some of the burden of choosing and adhering to the complex indexing conventions needed for staggered grids (in parallel)</p></li>
<li><p>To provide a uniform abstraction for which scalable solvers and preconditioners may be developed (in particular, using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCFIELDSPLIT.html">PCFIELDSPLIT</a></span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCMG.html">PCMG</a></span></code>).</p></li>
</ol>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> is design to behave much
like <a class="reference internal" href="vec.html#sec-struct"><span class="std std-ref">DMDA</span></a>, with a couple of important distinctions, and borrows some terminology
from <a class="reference internal" href="dmplex.html"><span class="doc">DMPLEX</span></a>.</p>
<section id="terminology">
<h2>Terminology<a class="headerlink" href="#terminology" title="Link to this heading">#</a></h2>
<p>Like a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPlex/DMPLEX.html">DMPLEX</a></span></code> object, a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> represents a <a class="reference external" href="https://en.wikipedia.org/wiki/CW_complex">cell complex</a>,
distributed in parallel over the ranks of an <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/MPI_Comm.html">MPI_Comm</a></span></code>. It is, however,
a very regular complex, consisting of a structured grid of <span class="math">\(d\)</span>-dimensional cells, with <span class="math">\(d \in \{1,2,3\}\)</span>,
which are referred to as <em>elements</em>, <span class="math">\(d-1\)</span> dimensional cells defining boundaries between these elements,
and the boundaries of the domain, and in 2 or more dimensions, boundaries of <em>these</em> cells,
all the way down to 0 dimensional cells referred to as <em>vertices</em>. In 2 dimensions, the 1-dimensional
element boundaries are referred to as <em>edges</em> or <em>faces</em>. In 3 dimensions, the 2-dimensional element boundaries
are referred to as <em>faces</em> and the 1-dimensional boundaries between faces are referred to as <em>edges</em>
The set of cells of a given dimension is referred to as a <em>stratum</em> (which one can think of as a level in DAG representation of the mesh); a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object of dimension <span class="math">\(d\)</span>
represents a complete cell complex with <span class="math">\(d+1\)</span> <em>strata</em> (levels).</p>
<p>In the description of any:<code class="docutils notranslate"><span class="pre">ch_unstructured</span></code> the cells at each level are referred to as <em>points</em>. Thus we adopt that terminology uniformly in PETSc and so furthermore in this document,
point will refer to a cell.</p>
<p>Each stratum has a constant number of unknowns (which may be zero) associated with each point (cell) on that level.
The distinct unknowns associated with each point are referred to as <em>components</em>.</p>
<p>The structured grid, is like with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code>, decomposed via a Cartesian product of decompositions in each dimension,
giving a rectangular local subdomain on each rank. This is extended by an element-wise stencil width
of <em>ghost</em> elements to create an atlas of overlapping patches.</p>
</section>
<section id="working-with-vectors-and-operators-matrices">
<h2>Working with vectors and operators (matrices)<a class="headerlink" href="#working-with-vectors-and-operators-matrices" title="Link to this heading">#</a></h2>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> allows the user to reason almost entirely about a global indexing of elements.
Element indices are simply 1-3 <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Sys/PetscInt.html">PetscInt</a></span></code> values, starting at <span class="math">\(0\)</span>, in the
back, bottom, left corner of the domain. For instance, element <span class="math">\((1,2,3)\)</span>, in 3D,
is the element second from the left, third from the bottom, and fourth from the back
(regardless of how many MPI ranks are used).</p>
<p>To refer to points (elements, faces, edges, and vertices), a value of
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMStagStencilLocation</a></span></code> is used, relative to the element index. The element
itself is referred to with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_ELEMENT</a></span></code>, the top right vertex (in 2D)
or the top right edge (in 3D) with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_UP_RIGHT</a></span></code>, the back bottom left
corner in 3D with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_BACK_DOWN_LEFT</a></span></code>, and so on.</p>
<p><a class="reference internal" href="#figure-dmstag-indexing"><span class="std std-numref">Fig. 10</span></a> gives a few examples in 2D.</p>
<figure class="align-default" id="figure-dmstag-indexing">
<img alt="../_images/dmstag_indexing.svg" src="../_images/dmstag_indexing.svg" /><figcaption>
<p><span class="caption-number">Fig. 10 </span><span class="caption-text">Locations in <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> are indexed according to global element indices (here, two in 2D) and a location name. Elements have unique names but other locations can be referred to in more than one way. Element colors correspond to a parallel decomposition, but locations on the grid have names which are invariant to this. Note that the face on the top right can be referred to as being to the left of a “dummy” element <span class="math">\((3,3)\)</span> outside the physical domain.</span><a class="headerlink" href="#figure-dmstag-indexing" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>Crucially, this global indexing scheme does not include any “ghost” or “padding” unknowns outside the physical domain.
This is useful for higher-level operations such as computing norms or developing physics-based solvers. However
(unlike <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code>), this implies that the global <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> do not have a natural block structure, as different
strata have different numbers of points (e.g. in 1D there is an “extra” vertex on the right). This regular block
structure is, however, very useful for the <em>local</em> representation of the data, so in that case <em>dummy</em> DOF
are included, drawn as grey in <a class="reference internal" href="#figure-dmstag-local-global"><span class="std std-numref">Fig. 11</span></a>.</p>
<figure class="align-default" id="figure-dmstag-local-global">
<img alt="../_images/dmstag_local_global.svg" src="../_images/dmstag_local_global.svg" /><figcaption>
<p><span class="caption-number">Fig. 11 </span><span class="caption-text">Local and global representations for a 2D <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object, 3 by 4 elements, with one degree of freedom on each of the three strata: element (squares), faces (triangles), and vertices (circles). The cell complex is parallelized across 4 MPI ranks. In the global representation, the colors correspond to which rank holds the native representation of the unknown. The 4 local representations are shown, with an (elementwise) stencil “box” stencil width of 1. Unknowns are colored by their native rank. Dummy unknowns, which correspond to no global degree of freedom, are colored grey. Note that the local representations have a natural block size of 4, and the global representation has no natural block size.</span><a class="headerlink" href="#figure-dmstag-local-global" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>For working with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> data, this approach is used to allow direct access to a multi-dimensional, regular-blocked
array. To avoid the user having to know about the <a class="reference internal" href="#sec-dmstag-numbering"><span class="std std-ref">internal numbering conventions used</span></a>,
helper functions are used to produce the proper final integer index for a given location and component, referred to as a “slot”.
Similarly to <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDAVecGetArrayDOF.html">DMDAVecGetArrayDOF</a>()</span></code>, this uses a <span class="math">\(d+1\)</span> dimensional array in <span class="math">\(d\)</span> dimensions.
The following snippet give an example of this usage.</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="w"> </span><span class="cm">/* Set the second component of all vertex dof to 2.0 */</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/DMStag/DMStagGetCorners.html">DMStagGetCorners</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">s_x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">s_y</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">s_z</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_y</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_z</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_e_x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_e_y</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">n_e_z</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/DMStag/DMStagGetLocationSlot.html">DMStagGetLocationSlot</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">location_vertex</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">slot_vertex_2</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/DMStag/DMStagVecGetArray.html">DMStagVecGetArray</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">x_array</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">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s_z</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">s_z</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_z</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_e_z</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">k</span><span class="p">)</span><span class="w"> </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">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s_y</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">s_y</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_y</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_e_y</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s_x</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">s_x</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_x</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n_e_x</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="n">x_array</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">][</span><span class="n">slot_vertex_2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="p">;</span>
<span class="w"> </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/DMStag/DMStagVecRestoreArray.html">DMStagVecRestoreArray</a></span><span class="p">(</span><span class="n">dm</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">x_array</span><span class="p">));</span>
</pre></div>
</div>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> provides a stencil-based method for getting and setting entries of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/Mat.html">Mat</a></span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> objects.
The follow excerpt from <a href="../src/dm/impls/stag/tutorials/ex1.c.html">DMSTAG Tutorial ex1</a> demonstrates
the idea. For more, see the manual page for <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagMatSetValuesStencil.html">DMStagMatSetValuesStencil</a>()</span></code>.</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="w"> </span><span class="cm">/* Velocity is either a BC or an interior point */</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFirstRank</span><span class="w"> </span><span class="o">&&</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">start</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../manualpages/DMStag/DMStagStencil.html">DMStagStencil</a></span><span class="w"> </span><span class="n">row</span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a></span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">e</span><span class="p">;</span>
<span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="n">loc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LEFT</span><span class="p">;</span>
<span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="n">c</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">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1.0</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/DMStag/DMStagMatSetValuesStencil.html">DMStagMatSetValuesStencil</a></span><span class="p">(</span><span class="n">dmSol</span><span class="p">,</span><span class="w"> </span><span class="n">A</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">row</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">row</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../manualpages/Sys/INSERT_VALUES.html">INSERT_VALUES</a></span><span class="p">));</span>
</pre></div>
</div>
<p>The array-based approach for <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code> is likely to be more efficient than the stencil-based method just introduced above.</p>
</section>
<section id="coordinates">
<h2>Coordinates<a class="headerlink" href="#coordinates" title="Link to this heading">#</a></h2>
<p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code>, unlike <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code>, supports two approaches to defining coordinates. This is captured by which type of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>
is used to represent the coordinates. No default is imposed, so the user must directly or indirectly call
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagSetCoordinateDMType.html">DMStagSetCoordinateDMType</a>()</span></code>.</p>
<p>If a second <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object is used to represent coordinates in “explicit” form, behavior is much like with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code> - the coordinate <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code>
has <span class="math">\(d\)</span> DOF on each stratum corresponding to coordinates associated with each point.</p>
<p>If <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPRODUCT/DMPRODUCT.html">DMPRODUCT</a></span></code> is used instead, coordinates are represented by a <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPRODUCT/DMPRODUCT.html">DMPRODUCT</a></span></code> object referring to a
Cartesian product of 1D <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> objects, each of which features explicit coordinates as just mentioned.</p>
<p>Navigating these nested <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DM/DM.html">DM</a></span></code> in <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMPRODUCT/DMPRODUCT.html">DMPRODUCT</a></span></code> can be tedious, but note the existence of helper functions like
<code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagSetUniformCoordinatesProduct.html">DMStagSetUniformCoordinatesProduct</a>()</span></code> and <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagGetProductCoordinateArrays.html">DMStagGetProductCoordinateArrays</a>()</span></code>.</p>
</section>
<section id="numberings-and-internal-data-layout">
<span id="sec-dmstag-numbering"></span><h2>Numberings and internal data layout<a class="headerlink" href="#numberings-and-internal-data-layout" title="Link to this heading">#</a></h2>
<p>While <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> aims to hide the details of its internal data layout, for debugging, optimization, and
customization purposes, it can be important to know how <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> internally numbers unknowns.</p>
<p>Internally, each point is canonically associated with an element (top-level point (cell)). For purposes of local,
regular-blocked storage, an element is grouped with lower-dimensional points left of, below (“down”), and behind (“back”) it.
This means that “canonical” values of <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMStagStencilLocation</a></span></code> are <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_ELEMENT</a></span></code>, plus all entries consisting only of “LEFT”, “DOWN”, and “BACK”. In general, these are the most efficient values to use, unless convenience dictates otherwise, as they are the ones used internally.</p>
<p>When creating the decomposition of the domain to local ranks, and extending these local domains to handle overlapping halo regions and boundary ghost unknowns, this same per-element association is used. This has the advantage of maintaining a regular blocking, but may not be optimal in some situations in terms of data movement.</p>
<p>Numberings are, like <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code>, based on a local “x-fastest, z-slowest” or “PETSc” ordering of elements (see <a class="reference internal" href="vec.html#sec-ao"><span class="std std-ref">Application Orderings</span></a>), with ordering of locations canonically associated with each element decided by considering unknowns on each point
to be located at the center of their point, and using a nested ordering of the same style. Thus, in 3-D, the ordering of the 8 canonical <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMStagStencilLocation</a></span></code> values associated
with an element is</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_BACK_DOWN_LEFT</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_BACK_DOWN</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_BACK_LEFT</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_BACK</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_DOWN_LEFT</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_DOWN</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_LEFT</a></span>
<span class="n"><a href="../manualpages/DMStag/DMStagStencilLocation.html">DMSTAG_ELEMENT</a></span>
</pre></div>
</div>
<p>Multiple DOF associated with a given point are stored sequentially (as with <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/DMDA.html">DMDA</a></span></code>).</p>
<p>For local <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Vec/Vec.html">Vec</a></span></code>s, this gives a regular-blocked numbering, with the same number of unknowns associated with each element, including some “dummy” unknowns which to not correspond to any (local or global) unknown in the global representation. See <a class="reference internal" href="#figure-dmstag-numbering-local"><span class="std std-numref">Fig. 13</span></a> for an example.</p>
<p>In the global representation, only physical unknowns are numbered (using the same “Z” ordering for unknowns which are present), giving irregular numbers of unknowns, depending on whether a domain boundary is present. See <a class="reference internal" href="#figure-dmstag-numbering-global"><span class="std std-numref">Fig. 12</span></a> for an example.</p>
<figure class="align-default" id="figure-dmstag-numbering-global">
<img alt="../_images/dmstag_numbering_global.svg" src="../_images/dmstag_numbering_global.svg" /><figcaption>
<p><span class="caption-number">Fig. 12 </span><span class="caption-text">Global numbering scheme for a 2D <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object with one DOF per stratum. Note that the numbering depends on the parallel decomposition (over 4 ranks, here).</span><a class="headerlink" href="#figure-dmstag-numbering-global" title="Link to this image">#</a></p>
</figcaption>
</figure>
<figure class="align-default" id="figure-dmstag-numbering-local">
<img alt="../_images/dmstag_numbering_local.svg" src="../_images/dmstag_numbering_local.svg" /><figcaption>
<p><span class="caption-number">Fig. 13 </span><span class="caption-text">Local numbering scheme on rank 1 (Cf. <a class="reference internal" href="#figure-dmstag-local-global"><span class="std std-numref">Fig. 11</span></a>) for a 2D <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> object with one DOF per stratum. Note that dummy locations (grey) are used to give a regular block size (here, 4).</span><a class="headerlink" href="#figure-dmstag-numbering-local" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>It should be noted that this is an <em>interlaced</em> (AoS) representation. If a segregated (SoA) representation is required,
one should use <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMComposite/DMCOMPOSITE.html">DMCOMPOSITE</a></span></code> collecting several <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> objects, perhaps using <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMStagCreateCompatibleDMStag.html">DMStagCreateCompatibleDMStag</a>()</span></code> to
quickly create additional <code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMStag/DMSTAG.html">DMSTAG</a></span></code> objects from an initial one.</p>
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