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<section class="tex2jax_ignore mathjax_ignore" id="pchpddm">
<h1>PCHPDDM<a class="headerlink" href="#pchpddm" title="Link to this heading">#</a></h1>
<p>Interface with the HPDDM library. This <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PC.html">PC</a></span></code> may be used to build multilevel spectral domain decomposition methods based on the GenEO framework <span id="id1">[<a class="reference internal" href="#id46" title="Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, and Robert Scheichl. A robust two-level domain decomposition preconditioner for systems of PDEs. Comptes Rendus Mathematique, 349(23-24):1255–1259, 2011.">SDH+11</a>]</span> <span id="id2">[<a class="reference internal" href="#id44" title="Hussam Al Daas, Laura Grigori, Pierre Jolivet, and Pierre-Henri Tournier. A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces. SIAM Journal on Scientific Computing, 43(3):A1907–A1928, 2021.">ADGJT21</a>]</span>.
It may be viewed as an alternative to spectral
AMGe or <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code> with adaptive selection of constraints. The interface is explained in details in <span id="id3">[<a class="reference internal" href="#id981" title="Pierre Jolivet, Jose Roman, and Stefano Zampini. KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners. Computers and Mathematics with Applications, 84:277–295, 2021.">JRZ21</a>]</span></p>
<p>The matrix used for building the preconditioner (Pmat) may be unassembled (<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATIS.html">MATIS</a></span></code>), assembled (<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, or <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>), hierarchical (<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATHTOOL.html">MATHTOOL</a></span></code>), <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATNORMAL.html">MATNORMAL</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATNORMALHERMITIAN.html">MATNORMALHERMITIAN</a></span></code>, or <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/MATSCHURCOMPLEMENT.html">MATSCHURCOMPLEMENT</a></span></code> (when <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDM.html">PCHPDDM</a></span></code> is used as part of an outer <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCFIELDSPLIT.html">PCFIELDSPLIT</a></span></code>).</p>
<p>For multilevel preconditioning, when using an assembled or hierarchical Pmat, one must provide an auxiliary local <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/Mat.html">Mat</a></span></code> (unassembled local operator for GenEO) using
<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetAuxiliaryMat.html">PCHPDDMSetAuxiliaryMat</a>()</span></code>. Calling this routine is not needed when using a <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATIS.html">MATIS</a></span></code> Pmat, assembly is done internally using <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MatConvert.html">MatConvert</a>()</span></code>.</p>
<section id="options-database-keys">
<h2>Options Database Keys<a class="headerlink" href="#options-database-keys" title="Link to this heading">#</a></h2>
<ul class="simple">
<li><p><em><strong>-pc_hpddm_define_subdomains <true, default=false> -</strong></em> on the finest level, calls <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCASMSetLocalSubdomains.html">PCASMSetLocalSubdomains</a>()</span></code> with the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/IS/IS.html">IS</a></span></code> supplied in <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetAuxiliaryMat.html">PCHPDDMSetAuxiliaryMat</a>()</span></code>
(not relevant with an unassembled Pmat)</p></li>
<li><p><em><strong>-pc_hpddm_has_neumann <true, default=false> -</strong></em> on the finest level, informs the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PC.html">PC</a></span></code> that the local Neumann matrix is supplied in <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetAuxiliaryMat.html">PCHPDDMSetAuxiliaryMat</a>()</span></code></p></li>
<li><p><em><strong>-pc_hpddm_coarse_correction <type, default=deflated> -</strong></em> determines the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMCoarseCorrectionType.html">PCHPDDMCoarseCorrectionType</a></span></code> when calling <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCApply.html">PCApply</a>()</span></code></p></li>
</ul>
<p>Options for subdomain solvers, subdomain eigensolvers (for computing deflation vectors), and the coarse solver can be set using the following options database prefixes.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> -pc_hpddm_levels_%d_pc_
-pc_hpddm_levels_%d_ksp_
-pc_hpddm_levels_%d_eps_
-pc_hpddm_levels_%d_p
-pc_hpddm_levels_%d_mat_type
-pc_hpddm_coarse_
-pc_hpddm_coarse_p
-pc_hpddm_coarse_mat_type
-pc_hpddm_coarse_mat_filter
</pre></div>
</div>
<p>E.g., -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 10 -pc_hpddm_levels_2_p 4 -pc_hpddm_levels_2_sub_pc_type lu -pc_hpddm_levels_2_eps_nev 10
-pc_hpddm_coarse_p 2 -pc_hpddm_coarse_mat_type baij will use 10 deflation vectors per subdomain on the fine “level 1”,
aggregate the fine subdomains into 4 “level 2” subdomains, then use 10 deflation vectors per subdomain on “level 2”,
and assemble the coarse matrix (of dimension 4 x 10 = 40) on two processes as a <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code> (default is <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>).</p>
<p>In order to activate a “level N+1” coarse correction, it is mandatory to call -pc_hpddm_levels_N_eps_nev <nu> or -pc_hpddm_levels_N_eps_threshold <val>. The default -pc_hpddm_coarse_p value is 1, meaning that the coarse operator is aggregated on a single process.</p>
</section>
<section id="notes">
<h2>Notes<a class="headerlink" href="#notes" title="Link to this heading">#</a></h2>
<p>This preconditioner requires that PETSc is built with SLEPc (<code class="docutils notranslate"><span class="pre">--download-slepc</span></code>).</p>
<p>By default, the underlying concurrent eigenproblems
are solved using SLEPc shift-and-invert spectral transformation. This is usually what gives the best performance for GenEO, cf.
<span id="id4">[<a class="reference internal" href="#id46" title="Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, and Robert Scheichl. A robust two-level domain decomposition preconditioner for systems of PDEs. Comptes Rendus Mathematique, 349(23-24):1255–1259, 2011.">SDH+11</a>]</span> <span id="id5">[<a class="reference internal" href="#id1057" title="Pierre Jolivet, Frédéric Hecht, Frédéric Nataf, and Christophe Prud'homme. Scalable domain decomposition preconditioners for heterogeneous elliptic problems. In Proceedings of SC13: International Conference for High Performance Computing, Networking, Storage and Analysis, 80. ACM, 2013.">JHNPrudhomme13</a>]</span>. As
stated above, SLEPc options are available through -pc_hpddm_levels_%d_, e.g., -pc_hpddm_levels_1_eps_type arpack -pc_hpddm_levels_1_eps_nev 10
-pc_hpddm_levels_1_st_type sinvert. There are furthermore three options related to the (subdomain-wise local) eigensolver that are not described in
SLEPc documentation since they are specific to <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDM.html">PCHPDDM</a></span></code>.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> -pc_hpddm_levels_1_st_share_sub_ksp
-pc_hpddm_levels_%d_eps_threshold
-pc_hpddm_levels_1_eps_use_inertia
</pre></div>
</div>
<p>The first option from the list only applies to the fine-level eigensolver, see <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetSTShareSubKSP.html">PCHPDDMSetSTShareSubKSP</a>()</span></code>. The second option from the list is
used to filter eigenmodes retrieved after convergence of <code class="docutils notranslate"><span class="pre">EPSSolve()</span></code> at “level N” such that eigenvectors used to define a “level N+1” coarse
correction are associated to eigenvalues whose magnitude are lower or equal than -pc_hpddm_levels_N_eps_threshold. When using an <code class="docutils notranslate"><span class="pre">EPS</span></code> which cannot
determine a priori the proper -pc_hpddm_levels_N_eps_nev such that all wanted eigenmodes are retrieved, it is possible to get an estimation of the
correct value using the third option from the list, -pc_hpddm_levels_1_eps_use_inertia, see <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MatGetInertia.html">MatGetInertia</a>()</span></code>. In that case, there is no need
to supply -pc_hpddm_levels_1_eps_nev. This last option also only applies to the fine-level (N = 1) eigensolver.</p>
<p>See also <span id="id6">[<a class="reference internal" href="#id45" title="Victorita Dolean, Pierre Jolivet, and Frédéric Nataf. An introduction to domain decomposition methods: algorithms, theory, and parallel implementation. SIAM, 2015.">DJN15</a>]</span>, <span id="id7">[<a class="reference internal" href="#id43" title="Hussam Al Daas, Pierre Jolivet, and Jennifer A Scott. A robust algebraic domain decomposition preconditioner for sparse normal equations. SIAM Journal on Scientific Computing, 44(3):A1047–A1068, 2022.">ADJS22</a>]</span>, <span id="id8">[<a class="reference internal" href="#id42" title="Hussam Al Daas and Pierre Jolivet. A robust algebraic multilevel domain decomposition preconditioner for sparse symmetric positive definite matrices. SIAM Journal on Scientific Computing, 44(4):A2582–A2598, 2022.">ADJ22</a>]</span>, and <span id="id9">[<a class="reference internal" href="#id41" title="Frédéric Nataf and Pierre-Henri Tournier. Recent advances in domain decomposition methods for large-scale saddle point problems. Comptes Rendus. Mécanique, 350(S1):1–15, 2022.">NT22</a>]</span></p>
</section>
<section id="references">
<h2>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h2>
<div class="docutils container" id="id10">
<div role="list" class="citation-list">
<div class="citation" id="id44" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">ADGJT21</a><span class="fn-bracket">]</span></span>
<p>Hussam Al Daas, Laura Grigori, Pierre Jolivet, and Pierre-Henri Tournier. A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces. <em>SIAM Journal on Scientific Computing</em>, 43(3):A1907–A1928, 2021.</p>
</div>
<div class="citation" id="id42" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id8">ADJ22</a><span class="fn-bracket">]</span></span>
<p>Hussam Al Daas and Pierre Jolivet. A robust algebraic multilevel domain decomposition preconditioner for sparse symmetric positive definite matrices. <em>SIAM Journal on Scientific Computing</em>, 44(4):A2582–A2598, 2022.</p>
</div>
<div class="citation" id="id43" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id7">ADJS22</a><span class="fn-bracket">]</span></span>
<p>Hussam Al Daas, Pierre Jolivet, and Jennifer A Scott. A robust algebraic domain decomposition preconditioner for sparse normal equations. <em>SIAM Journal on Scientific Computing</em>, 44(3):A1047–A1068, 2022.</p>
</div>
<div class="citation" id="id45" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id6">DJN15</a><span class="fn-bracket">]</span></span>
<p>Victorita Dolean, Pierre Jolivet, and Frédéric Nataf. <em>An introduction to domain decomposition methods: algorithms, theory, and parallel implementation</em>. SIAM, 2015.</p>
</div>
<div class="citation" id="id1057" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">JHNPrudhomme13</a><span class="fn-bracket">]</span></span>
<p>Pierre Jolivet, Frédéric Hecht, Frédéric Nataf, and Christophe Prud'homme. Scalable domain decomposition preconditioners for heterogeneous elliptic problems. In <em>Proceedings of SC13: International Conference for High Performance Computing, Networking, Storage and Analysis</em>, 80. ACM, 2013.</p>
</div>
<div class="citation" id="id981" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">JRZ21</a><span class="fn-bracket">]</span></span>
<p>Pierre Jolivet, Jose Roman, and Stefano Zampini. KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners. <em>Computers and Mathematics with Applications</em>, 84:277–295, 2021.</p>
</div>
<div class="citation" id="id41" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id9">NT22</a><span class="fn-bracket">]</span></span>
<p>Frédéric Nataf and Pierre-Henri Tournier. Recent advances in domain decomposition methods for large-scale saddle point problems. <em>Comptes Rendus. Mécanique</em>, 350(S1):1–15, 2022.</p>
</div>
<div class="citation" id="id46" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>SDH+11<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id4">2</a>)</span>
<p>Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, and Robert Scheichl. A robust two-level domain decomposition preconditioner for systems of PDEs. <em>Comptes Rendus Mathematique</em>, 349(23-24):1255–1259, 2011.</p>
</div>
</div>
</div>
</section>
<section id="see-also">
<h2>See Also<a class="headerlink" href="#see-also" title="Link to this heading">#</a></h2>
<p><a class="reference internal" href="../../manual/ksp.html#ch-ksp"><span class="std std-ref">KSP: Linear System Solvers</span></a>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCCreate.html">PCCreate</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCSetType.html">PCSetType</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCType.html">PCType</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/PC/PCHPDDMSetAuxiliaryMat.html">PCHPDDMSetAuxiliaryMat</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATIS.html">MATIS</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCDEFLATION.html">PCDEFLATION</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCTELESCOPE.html">PCTELESCOPE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCASM.html">PCASM</a></span></code>,
<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetCoarseCorrectionType.html">PCHPDDMSetCoarseCorrectionType</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMHasNeumannMat.html">PCHPDDMHasNeumannMat</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetRHSMat.html">PCHPDDMSetRHSMat</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetDeflationMat.html">PCHPDDMSetDeflationMat</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMSetSTShareSubKSP.html">PCHPDDMSetSTShareSubKSP</a>()</span></code>,
<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMGetSTShareSubKSP.html">PCHPDDMGetSTShareSubKSP</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMGetCoarseCorrectionType.html">PCHPDDMGetCoarseCorrectionType</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCHPDDMGetComplexities.html">PCHPDDMGetComplexities</a>()</span></code></p>
</section>
<section id="level">
<h2>Level<a class="headerlink" href="#level" title="Link to this heading">#</a></h2>
<p>intermediate</p>
</section>
<section id="location">
<h2>Location<a class="headerlink" href="#location" title="Link to this heading">#</a></h2>
<p><A HREF="../../src/ksp/pc/impls/hpddm/pchpddm.cxx.html#PCHPDDM">src/ksp/pc/impls/hpddm/pchpddm.cxx</A></p>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading">#</a></h2>
<p><A HREF="../../src/ksp/ksp/tutorials/ex76f.F90.html">src/ksp/ksp/tutorials/ex76f.F90</A><BR>
<A HREF="../../src/ksp/ksp/tutorials/ex87.c.html">src/ksp/ksp/tutorials/ex87.c</A><BR>
<A HREF="../../src/snes/tutorials/ex12.c.html">src/snes/tutorials/ex12.c</A><BR>
<A HREF="../../src/ksp/ksp/tutorials/ex27.c.html">src/ksp/ksp/tutorials/ex27.c</A><BR>
<A HREF="../../src/ksp/ksp/tutorials/ex76.c.html">src/ksp/ksp/tutorials/ex76.c</A><BR>
<A HREF="../../src/ksp/ksp/tutorials/ex82.c.html">src/ksp/ksp/tutorials/ex82.c</A><BR></p>
<hr class="docutils" />
<p><a class="reference internal" href="index.html"><span class="std std-doc">Index of all PC routines</span></a><br />
<a class="reference internal" href="../index.html"><span class="std std-doc">Table of Contents for all manual pages</span></a><br />
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