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<section class="tex2jax_ignore mathjax_ignore" id="kspfetidp">
<h1>KSPFETIDP<a class="headerlink" href="#kspfetidp" title="Link to this heading">#</a></h1>
<p>The FETI-DP method <span id="id1">[<a class="reference internal" href="#id70" title="Charbel Farhat, Michel Lesoinne, Patrick LeTallec, Kendall Pierson, and Daniel Rixen. FETI-DP: a dual–primal unified FETI method—part I: a faster alternative to the two-level FETI method. International journal for numerical methods in engineering, 50(7):1523–1544, 2001.">FLL+01</a>]</span></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>-ksp_fetidp_fullyredundant <false> -</strong></em> use a fully redundant set of Lagrange multipliers</p></li>
<li><p><em><strong>-ksp_fetidp_saddlepoint <false> -</strong></em> activates support for saddle point problems, see <span id="id2">[<a class="reference internal" href="#id69" title="Xuemin Tu and Jing Li. A FETI-DP type domain decomposition algorithm for three-dimensional incompressible Stokes equations. SIAM Journal on Numerical Analysis, 53(2):720–742, 2015.">TL15</a>]</span></p></li>
<li><p><em><strong>-ksp_fetidp_saddlepoint_flip <false> -</strong></em> see note below</p></li>
<li><p><em><strong>-ksp_fetidp_pressure_field <-</strong></em> 1> - activates support for saddle point problems, and identifies the pressure field id.
If this information is not provided, the pressure field is detected by using <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MatFindZeroDiagonals.html">MatFindZeroDiagonals</a>()</span></code>.</p></li>
<li><p><em><strong>-ksp_fetidp_pressure_all <false> -</strong></em> if false, uses the interface pressures, as described in [2]. If true, uses the entire pressure field.</p></li>
</ul>
</section>
<section id="notes">
<h2>Notes<a class="headerlink" href="#notes" title="Link to this heading">#</a></h2>
<p>The matrix for the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> must be of type <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/Mat/MATIS.html">MATIS</a></span></code>.</p>
<p>Usually, an incompressible Stokes problem is written as</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> | A B^T | | v | = | f |
| B 0 | | p | = | g |
</pre></div>
</div>
<p>with B representing <span class="math">\( -\int_\Omega \nabla \cdot u q \)</span>. If -ksp_fetidp_saddlepoint_flip is true, the code assumes that the user provides it as</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> | A B^T | | v | = | f |
|-B 0 | | p | = |-g |
</pre></div>
</div>
<p>The FETI-DP linear system (automatically generated constructing an internal <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code> object) is solved using an internal <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> object.</p>
<p>Options for the inner <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> and for the customization of the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code> object can be specified at command line by using the prefixes <code class="docutils notranslate"><span class="pre">-fetidp_</span></code> and <code class="docutils notranslate"><span class="pre">-fetidp_bddc_</span></code>. E.g.,</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> -fetidp_ksp_type gmres -fetidp_bddc_pc_bddc_symmetric false
</pre></div>
</div>
<p>will use <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPGMRES.html">KSPGMRES</a></span></code> for the solution of the linear system on the Lagrange multipliers, generated using a non-symmetric <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code>.</p>
<p>For saddle point problems with continuous pressures, the preconditioned operator for the pressure solver can be specified with <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPFETIDPSetPressureOperator.html">KSPFETIDPSetPressureOperator</a>()</span></code>.
Alternatively, the pressure operator is extracted from the precondioned matrix (if it is different from the linear solver matrix).
If none of the above, an identity matrix will be created; the user then needs to scale it through a Richardson solver.
Options for the pressure solver can be prefixed with <code class="docutils notranslate"><span class="pre">-fetidp_fielsplit_p_</span></code>, E.g.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> -fetidp_fielsplit_p_ksp_type preonly -fetidp_fielsplit_p_pc_type lu -fetidp_fielsplit_p_pc_factor_mat_solver_type mumps
</pre></div>
</div>
<p>In order to use the deluxe version of FETI-DP, you must customize the inner <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code> operator with -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat and use
non-redundant multipliers, i.e. <code class="docutils notranslate"><span class="pre">-ksp_fetidp_fullyredundant</span> <span class="pre">false</span></code>. Options for the scaling solver are prefixed by <code class="docutils notranslate"><span class="pre">-fetidp_bddelta_</span></code>, E.g.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span> -fetidp_bddelta_pc_factor_mat_solver_type mumps -fetidp_bddelta_pc_type lu
</pre></div>
</div>
<p>Some of the basic options such as the maximum number of iterations and tolerances are automatically passed from this <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> to the inner <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> that actually performs the iterations.</p>
<p>The converged reason and number of iterations computed are passed from the inner <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> to this <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> at the end of the solution.</p>
</section>
<section id="developer-note">
<h2>Developer Note<a class="headerlink" href="#developer-note" title="Link to this heading">#</a></h2>
<p>Even though this method does not directly use any norms, the user is allowed to set the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPNormType.html">KSPNormType</a></span></code> to any value.
This is so users do not have to change <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPNormType.html">KSPNormType</a></span></code> options when they switch from other <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSP.html">KSP</a></span></code> methods to this one.</p>
</section>
<section id="references">
<h2>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h2>
<div class="docutils container" id="id3">
<div role="list" class="citation-list">
<div class="citation" id="id70" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">FLL+01</a><span class="fn-bracket">]</span></span>
<p>Charbel Farhat, Michel Lesoinne, Patrick LeTallec, Kendall Pierson, and Daniel Rixen. FETI-DP: a dual–primal unified FETI method—part I: a faster alternative to the two-level FETI method. <em>International journal for numerical methods in engineering</em>, 50(7):1523–1544, 2001.</p>
</div>
<div class="citation" id="id69" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">TL15</a><span class="fn-bracket">]</span></span>
<p>Xuemin Tu and Jing Li. A FETI-DP type domain decomposition algorithm for three-dimensional incompressible Stokes equations. <em>SIAM Journal on Numerical Analysis</em>, 53(2):720–742, 2015.</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/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/KSP/KSPFETIDPSetInnerBDDC.html">KSPFETIDPSetInnerBDDC</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPFETIDPGetInnerBDDC.html">KSPFETIDPGetInnerBDDC</a>()</span></code>, <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/KSP/KSPFETIDPGetInnerKSP.html">KSPFETIDPGetInnerKSP</a>()</span></code></p>
</section>
<section id="level">
<h2>Level<a class="headerlink" href="#level" title="Link to this heading">#</a></h2>
<p>Advanced</p>
</section>
<section id="location">
<h2>Location<a class="headerlink" href="#location" title="Link to this heading">#</a></h2>
<p><A HREF="../../src/ksp/ksp/impls/fetidp/fetidp.c.html#KSPFETIDP">src/ksp/ksp/impls/fetidp/fetidp.c</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/ex59.c.html">src/ksp/ksp/tutorials/ex59.c</A><BR></p>
<hr class="docutils" />
<p><a class="reference internal" href="index.html"><span class="std std-doc">Index of all KSP 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 />
<a class="reference internal" href="../singleindex.html"><span class="std std-doc">Index of all manual pages</span></a></p>
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