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<li class="toctree-l2"><a class="reference internal" href="Developer_utils.html#communication-buffer-coding-with-ubuf">4.22. Communication buffer coding with <em>ubuf</em></a></li>
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<li class="toctree-l2"><a class="reference internal" href="Developer_grid.html">4.23. Use of distributed grids within style classes</a></li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="partitioning">
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<h1><span class="section-number">4.4.1. </span>Partitioning<a class="headerlink" href="#partitioning" title="Link to this heading"></a></h1>
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<p>The underlying spatial decomposition strategy used by LAMMPS for
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distributed-memory parallelism is set with the <a class="reference internal" href="comm_style.html"><span class="doc">comm_style command</span></a> and can be either “brick” (a regular grid) or “tiled”.</p>
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<figure class="align-default" id="id1">
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<span id="domain-decomposition"></span><img alt="_images/domain-decomp.png" src="_images/domain-decomp.png" />
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<figcaption>
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<p><span class="caption-text">Domain decomposition schemes</span><a class="headerlink" href="#id1" title="Link to this image"></a></p>
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<div class="legend">
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<blockquote>
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<div><p>This figure shows the different kinds of domain decomposition used
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for MPI parallelization: “brick” on the left with an orthogonal
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(left) and a triclinic (middle) simulation domain, and a “tiled”
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decomposition (right). The black lines show the division into
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subdomains, and the contained atoms are “owned” by the
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corresponding MPI process. The green dashed lines indicate how
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subdomains are extended with “ghost” atoms up to the communication
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cutoff distance.</p>
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</div></blockquote>
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</div>
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</figcaption>
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</figure>
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<p>The LAMMPS simulation box is a 3d or 2d volume, which can be of
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orthogonal or triclinic shape, as illustrated in the
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<a class="reference internal" href="#domain-decomposition"><span class="std std-ref">Domain decomposition schemes</span></a> figure for the 2d case. Orthogonal means
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the box edges are aligned with the <em>x</em>, <em>y</em>, <em>z</em> Cartesian axes, and the
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box faces are thus all rectangular. Triclinic allows for a more general
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parallelepiped shape in which edges are aligned with three arbitrary
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vectors and the box faces are parallelograms. In each dimension, box
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faces can be periodic, or non-periodic with fixed or shrink-wrapped
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boundaries. In the fixed case, atoms which move outside the face are
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deleted; shrink-wrapped means the position of the box face adjusts
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continuously to enclose all the atoms.</p>
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<p>For distributed-memory MPI parallelism, the simulation box is spatially
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decomposed (partitioned) into non-overlapping subdomains which fill the
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box. The default partitioning, “brick”, is most suitable when atom
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density is roughly uniform, as shown in the left-side images of the
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<a class="reference internal" href="#domain-decomposition"><span class="std std-ref">Domain decomposition schemes</span></a> figure. The subdomains comprise a regular
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grid, and all subdomains are identical in size and shape. Both the
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orthogonal and triclinic boxes can deform continuously during a
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simulation, e.g. to compress a solid or shear a liquid, in which case
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the processor subdomains likewise deform.</p>
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<p>For models with non-uniform density, the number of particles per
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processor can be load-imbalanced with the default partitioning. This
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reduces parallel efficiency, as the overall simulation rate is limited
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by the slowest processor, i.e. the one with the largest computational
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load. For such models, LAMMPS supports multiple strategies to reduce
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the load imbalance:</p>
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<ul class="simple">
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<li><p>The processor grid decomposition is by default based on the simulation
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cell volume and tries to optimize the volume to surface ratio for the subdomains.
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This can be changed with the <a class="reference internal" href="processors.html"><span class="doc">processors command</span></a>.</p></li>
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<li><p>The parallel planes defining the size of the subdomains can be shifted
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with the <a class="reference internal" href="balance.html"><span class="doc">balance command</span></a>. Which can be done in addition
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to choosing a more optimal processor grid.</p></li>
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<li><p>The recursive bisectioning algorithm in combination with the “tiled”
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communication style can produce a partitioning with equal numbers of
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particles in each subdomain.</p></li>
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</ul>
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<p><a class="reference internal" href="_images/decomp-regular.png"><img alt="decomp1" src="_images/decomp-regular.png" style="width: 24%;" /></a> <a class="reference internal" href="_images/decomp-processors.png"><img alt="decomp2" src="_images/decomp-processors.png" style="width: 24%;" /></a> <a class="reference internal" href="_images/decomp-balance.png"><img alt="decomp3" src="_images/decomp-balance.png" style="width: 24%;" /></a> <a class="reference internal" href="_images/decomp-rcb.png"><img alt="decomp4" src="_images/decomp-rcb.png" style="width: 24%;" /></a></p>
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<p>The pictures above demonstrate different decompositions for a 2d system
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with 12 MPI ranks. The atom colors indicate the load imbalance of each
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subdomain, with green being optimal and red the least optimal.</p>
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<p>Due to the vacuum in the system, the default decomposition is
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unbalanced, with several MPI ranks without atoms (left). By forcing a
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1x12x1 processor grid, every MPI rank does computations now, but the
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number of atoms per subdomain is still uneven, and the thin slice shape
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increases the amount of communication between subdomains (center
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left). With a 2x6x1 processor grid and shifting the subdomain divisions,
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the load imbalance is further reduced and the amount of communication
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required between subdomains is less (center right). And using the
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recursive bisectioning leads to further improved decomposition (right).</p>
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