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4 years ago
<head><title>Method set</title>
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4 years ago
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class="cmr-12">[</span><a
4 years ago
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<h4 class="subsectionHead"><span class="titlemark"><span
4 years ago
class="cmr-12">5.2 </span></span> <a
id="x17-160005.2"></a><span
class="cmr-12">Method set</span></h4>
<div class="center"
>
4 years ago
<!--l. 74--><p class="noindent" >
<!--l. 75--><p class="noindent" ><span class="lstinline"></span><span
4 years ago
class="cmtt-12">call</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">p</span><span
class="cmtt-12">%</span><span
class="cmtt-12">set</span><span
class="cmtt-12">(</span><span
class="cmtt-12">what</span><span
class="cmtt-12">,</span><span
class="cmtt-12">val</span><span
class="cmtt-12">,</span><span
class="cmtt-12">info</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">[,</span><span
class="cmtt-12">ilev</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">ilmax</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">pos</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">idx</span><span
class="cmtt-12">])</span></div>
4 years ago
<!--l. 78--><p class="noindent" ><span
class="cmr-12">This method sets the parameters defining the preconditioner </span><span class="lstinline"></span><span
class="cmtt-12">p</span><span
4 years ago
class="cmr-12">. More precisely, the</span>
<span
class="cmr-12">parameter identified by </span><span class="lstinline"></span><span
class="cmtt-12">what</span> <span
class="cmr-12">is assigned the value contained in </span><span class="lstinline"></span><span
class="cmtt-12">val</span><span
4 years ago
class="cmr-12">.</span>
4 years ago
<!--l. 83--><p class="noindent" ><span
4 years ago
class="cmbx-12">Arguments</span>
<div class="tabular"> <table id="TBL-3" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-3-1g"><col
id="TBL-3-1"><col
id="TBL-3-2"></colgroup><tr
style="vertical-align:baseline;" id="TBL-3-1-"><td style="white-space:wrap; text-align:left;" id="TBL-3-1-1"
4 years ago
class="td11"><!--l. 86--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">what</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-1-2"
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class="td11"><!--l. 86--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">character</span><span
class="cmtt-12">(</span><span
class="cmtt-12">len</span><span
class="cmtt-12">=*)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-2-"><td style="white-space:wrap; text-align:left;" id="TBL-3-2-1"
class="td11"><!--l. 87--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-2-2"
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class="td11"><!--l. 87--><p class="noindent" ><span
4 years ago
class="cmr-12">The parameter to be set. It can be specified through its name; the</span>
<span
4 years ago
class="cmr-12">string is case-insensitive. See Tables</span><span
class="cmr-12">&#x00A0;</span><a
href="#x17-16009r2"><span
4 years ago
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
class="cmr-12">-</span><a
href="#x17-16014r7"><span
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-3-"><td style="white-space:wrap; text-align:left;" id="TBL-3-3-1"
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class="td11"><!--l. 90--><p class="noindent" ><span class="lstinline"></span><span
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class="cmtt-12">val</span><span
class="cmtt-12">&#x00A0;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-3-2"
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class="td11"><!--l. 90--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span> <span
class="cmti-12">or </span><span class="lstinline"></span><span
class="cmtt-12">character</span><span
class="cmtt-12">(</span><span
class="cmtt-12">len</span><span
class="cmtt-12">=*)</span> <span
class="cmti-12">or </span><span class="lstinline"></span><span
class="cmtt-12">real</span><span
class="cmtt-12">(</span><span
class="cmtt-12">psb_spk_</span><span
class="cmtt-12">)</span> <span
4 years ago
class="cmti-12">or</span>
<span class="lstinline"></span><span
class="cmtt-12">real</span><span
class="cmtt-12">(</span><span
class="cmtt-12">psb_dpk_</span><span
class="cmtt-12">)</span><span
class="cmr-12">, </span><span class="lstinline"></span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-4-"><td style="white-space:wrap; text-align:left;" id="TBL-3-4-1"
class="td11"><!--l. 93--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-4-2"
4 years ago
class="td11"><!--l. 93--><p class="noindent" ><span
4 years ago
class="cmr-12">The value of the parameter to be set. The list of allowed values and</span>
<span
class="cmr-12">the corresponding data types is given in Tables</span><span
class="cmr-12">&#x00A0;</span><a
href="#x17-16009r2"><span
4 years ago
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
class="cmr-12">-</span><a
href="#x17-16014r7"><span
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
4 years ago
class="cmr-12">. When the value</span>
<span
class="cmr-12">is of type </span><span class="lstinline"></span><span
class="cmtt-12">character</span><span
class="cmtt-12">(</span><span
class="cmtt-12">len</span><span
class="cmtt-12">=*)</span><span
4 years ago
class="cmr-12">, it is also treated as case insensitive.</span></td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-5-"><td style="white-space:wrap; text-align:left;" id="TBL-3-5-1"
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class="td11"><!--l. 98--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">info</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-5-2"
4 years ago
class="td11"><!--l. 98--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">out</span><span
class="cmtt-12">)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-6-"><td style="white-space:wrap; text-align:left;" id="TBL-3-6-1"
class="td11"><!--l. 99--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-6-2"
4 years ago
class="td11"><!--l. 99--><p class="noindent" ><span
4 years ago
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
class="cmr-12">&#x00A0;</span><a
href="userhtmlse7.html#x26-300007"><span
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
class="cmr-12">for details.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-7-"><td style="white-space:wrap; text-align:left;" id="TBL-3-7-1"
4 years ago
class="td11"><!--l. 101--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">ilev</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-7-2"
4 years ago
class="td11"><!--l. 101--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-8-"><td style="white-space:wrap; text-align:left;" id="TBL-3-8-1"
class="td11"><!--l. 102--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-8-2"
4 years ago
class="td11"><!--l. 102--><p class="noindent" ><span
4 years ago
class="cmr-12">For the multilevel preconditioner, the level at which the</span>
<span
class="cmr-12">preconditioner parameter has to be set. The levels are numbered</span>
<span
class="cmr-12">in increasing order starting from the finest one, i.e., level 1 is the</span>
<span
class="cmr-12">finest level. If </span><span class="lstinline"></span><span
class="cmtt-12">ilev</span> <span
class="cmr-12">is not present, the parameter identified by </span><span class="lstinline"></span><span
class="cmtt-12">what</span>
4 years ago
<span
4 years ago
class="cmr-12">is set at all levels that are appropriate (see Tables</span><span
4 years ago
class="cmr-12">&#x00A0;</span><a
href="#x17-16009r2"><span
4 years ago
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
class="cmr-12">-</span><a
href="#x17-16014r7"><span
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
4 years ago
class="cmr-12">).</span> </td>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-3-9-"><td style="white-space:wrap; text-align:left;" id="TBL-3-9-1"
4 years ago
class="td11"><!--l. 109--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">ilmax</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-9-2"
4 years ago
class="td11"><!--l. 109--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-10-"><td style="white-space:wrap; text-align:left;" id="TBL-3-10-1"
class="td11"><!--l. 110--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-10-2"
4 years ago
class="td11"><!--l. 110--><p class="noindent" ><span
class="cmr-12">For the multilevel preconditioner, when both </span><span class="lstinline"></span><span
class="cmtt-12">ilev</span> <span
class="cmr-12">and </span><span class="lstinline"></span><span
class="cmtt-12">ilmax</span> <span
4 years ago
class="cmr-12">are</span>
<span
class="cmr-12">present, the settings are applied at all levels </span><span class="lstinline"></span><span
class="cmtt-12">ilev</span><span
class="cmtt-12">:</span><span
class="cmtt-12">ilmax</span><span
4 years ago
class="cmr-12">. When</span>
<span class="lstinline"></span><span
class="cmtt-12">ilev</span> <span
class="cmr-12">is present but </span><span class="lstinline"></span><span
class="cmtt-12">ilmax</span> <span
class="cmr-12">is not, then the default is </span><span class="lstinline"></span><span
class="cmtt-12">ilmax</span><span
class="cmtt-12">=</span><span
class="cmtt-12">ilev</span><span
4 years ago
class="cmr-12">.</span>
<span
class="cmr-12">The levels are numbered in increasing order starting from the finest</span>
<span
class="cmr-12">one, i.e., level 1 is the finest level.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-11-"><td style="white-space:wrap; text-align:left;" id="TBL-3-11-1"
4 years ago
class="td11"><!--l. 117--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">pos</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-11-2"
4 years ago
class="td11"><!--l. 117--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">character</span><span
class="cmtt-12">(</span><span
class="cmtt-12">len</span><span
class="cmtt-12">=*),</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
class="cmr-12">.</span> </td>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-3-12-"><td style="white-space:wrap; text-align:left;" id="TBL-3-12-1"
class="td11"><!--l. 118--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-12-2"
4 years ago
class="td11"><!--l. 118--><p class="noindent" ><span
4 years ago
class="cmr-12">Whether the other arguments apply only to the pre-smoother</span>
<span
class="cmr-12">(</span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">PRE</span><span
class="cmtt-12">&#8217;</span><span
class="cmr-12">) or to the post-smoother (</span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">POST</span><span
class="cmtt-12">&#8217;</span><span
class="cmr-12">). If </span><span class="lstinline"></span><span
class="cmtt-12">pos</span> <span
4 years ago
class="cmr-12">is not present,</span>
<span
class="cmr-12">the other arguments are applied to both smoothers. If the</span>
<span
class="cmr-12">preconditioner is one-level or the parameter identified by </span><span class="lstinline"></span><span
class="cmtt-12">what</span> <span
4 years ago
class="cmr-12">does</span>
<span
class="cmr-12">not concern the smoothers, </span><span class="lstinline"></span><span
class="cmtt-12">pos</span> <span
4 years ago
class="cmr-12">is ignored.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-13-"><td style="white-space:wrap; text-align:left;" id="TBL-3-13-1"
4 years ago
class="td11"><!--l. 123--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">idx</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-13-2"
4 years ago
class="td11"><!--l. 123--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-12">integer</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">optional</span><span
class="cmtt-12">,</span><span
class="cmtt-12">&#x00A0;</span><span
class="cmtt-12">intent</span><span
class="cmtt-12">(</span><span
class="cmtt-12">in</span><span
class="cmtt-12">)</span><span
4 years ago
class="cmr-12">.</span> </td>
</tr><tr
style="vertical-align:baseline;" id="TBL-3-14-"><td style="white-space:wrap; text-align:left;" id="TBL-3-14-1"
class="td11"><!--l. 124--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-14-2"
4 years ago
class="td11"><!--l. 124--><p class="noindent" ><span
4 years ago
class="cmr-12">An auxiliary input argument that can be passed to the underlying</span>
<span
class="cmr-12">objects.</span> </td>
</tr></table></div>
4 years ago
<!--l. 129--><p class="noindent" >
<!--l. 134--><p class="indent" > <span
class="cmr-12">A variety of preconditioners can be obtained by setting the appropriate</span>
4 years ago
<span
class="cmr-12">preconditioner parameters. These parameters can be logically divided into four groups,</span>
<span
class="cmr-12">i.e., parameters defining</span>
<ol class="enumerate1" >
<li
class="enumerate" id="x17-16002x1"><span
class="cmr-12">the type of multilevel cycle and how many cycles must be applied;</span>
</li>
4 years ago
<li
class="enumerate" id="x17-16004x2"><span
class="cmr-12">the coarsening algorithm;</span>
</li>
4 years ago
<li
class="enumerate" id="x17-16006x3"><span
class="cmr-12">the coarse-space correction at the coarsest level (for multilevel</span>
<span
4 years ago
class="cmr-12">preconditioners only);</span>
4 years ago
</li>
4 years ago
<li
class="enumerate" id="x17-16008x4"><span
class="cmr-12">the smoother of the multilevel preconditioners, or the one-level</span>
<span
4 years ago
class="cmr-12">preconditioner.</span></li></ol>
<!--l. 145--><p class="noindent" ><span
4 years ago
class="cmr-12">A list of the parameters that can be set, along with their allowed and default values, is</span>
<span
4 years ago
class="cmr-12">given in Tables</span><span
class="cmr-12">&#x00A0;</span><a
href="#x17-16009r2"><span
4 years ago
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
class="cmr-12">-</span><a
href="#x17-16014r7"><span
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
4 years ago
class="cmr-12">.</span><br
class="newline" />
4 years ago
<!--l. 148--><p class="indent" > <span
4 years ago
class="cmbx-12">Remark 2. </span><span
class="cmr-12">A smoother is usually obtained by combining two objects: a</span>
<span
class="cmr-12">smoother (</span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">SMOOTHER_TYPE</span><span
class="cmtt-12">&#8217;</span><span
class="cmr-12">) and a local solver (</span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">SUB_SOLVE</span><span
class="cmtt-12">&#8217;</span><span
4 years ago
class="cmr-12">), as specified in</span>
<span
4 years ago
class="cmr-12">Tables</span><span
4 years ago
class="cmr-12">&#x00A0;</span><a
href="#x17-16013r6"><span
class="cmr-12">6</span><!--tex4ht:ref: tab:p_smoother --></a><span
4 years ago
class="cmr-12">-</span><a
href="#x17-16014r7"><span
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
4 years ago
class="cmr-12">. For example, the block-Jacobi smoother using ILU(0) on the blocks is</span>
<span
4 years ago
class="cmr-12">obtained by combining the block-Jacobi smoother object with the ILU(0) solver</span>
<span
4 years ago
class="cmr-12">object. Similarly, the hybrid Gauss-Seidel smoother (see Note in Table</span><span
4 years ago
class="cmr-12">&#x00A0;</span><a
href="#x17-16013r6"><span
class="cmr-12">6</span><!--tex4ht:ref: tab:p_smoother --></a><span
4 years ago
class="cmr-12">) is</span>
<span
4 years ago
class="cmr-12">obtained by combining the block-Jacobi smoother object with a single sweep of</span>
4 years ago
<span
4 years ago
class="cmr-12">the Gauss-Seidel solver object, while the point-Jacobi smoother is the result</span>
4 years ago
<span
4 years ago
class="cmr-12">of combining the block-Jacobi smoother object with a single sweep of the</span>
4 years ago
<span
4 years ago
class="cmr-12">point-Jacobi solver object. However, for simplicity, shortcuts are provided to set</span>
4 years ago
<span
4 years ago
class="cmr-12">point-Jacobi, hybrid (forward) Gauss-Seidel, and hybrid backward Gauss-Seidel, i.e.,</span>
<span
class="cmr-12">the previous smoothers can be defined just by setting </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">SMOOTHER_TYPE</span><span
class="cmtt-12">&#8217;</span> <span
4 years ago
class="cmr-12">to</span>
<span
class="cmr-12">certain specific values (see Tables</span><span
4 years ago
class="cmr-12">&#x00A0;</span><a
href="#x17-16013r6"><span
class="cmr-12">6</span><!--tex4ht:ref: tab:p_smoother --></a><span
4 years ago
class="cmr-12">), without the need to set </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">SUB_SOLVE</span><span
class="cmtt-12">&#8217;</span> <span
4 years ago
class="cmr-12">as</span>
<span
class="cmr-12">well.</span>
<!--l. 165--><p class="indent" > <span
4 years ago
class="cmr-12">The smoother and solver objects are arranged in a hierarchical manner. When</span>
<span
class="cmr-12">specifying a smoother object, its parameters, including the local solver, are set to</span>
<span
class="cmr-12">their default values, and when a solver object is specified, its defaults are also</span>
<span
class="cmr-12">set, overriding in both cases any previous settings even if explicitly specified.</span>
<span
class="cmr-12">Therefore if the user sets a smoother, and wishes to use a solver different from</span>
<span
class="cmr-12">the default one, the call to set the solver must come </span><span
class="cmti-12">after </span><span
class="cmr-12">the call to set the</span>
<span
4 years ago
class="cmr-12">smoother.</span>
4 years ago
<!--l. 174--><p class="indent" > <span
4 years ago
class="cmr-12">Similar considerations apply to the point-Jacobi, Gauss-Seidel and block-Jacobi</span>
<span
class="cmr-12">coarsest-level solvers, and shortcuts are available in this case too (see Table</span><span
class="cmr-12">&#x00A0;</span><span
class="cmbx-12">??</span><span
4 years ago
class="cmr-12">).</span>
<br
class="newline" />
4 years ago
<!--l. 178--><p class="indent" > <span
4 years ago
class="cmbx-12">Remark 3. </span><span
4 years ago
class="cmr-12">Many of the coarsest-level solvers cannot be used with both the</span>
4 years ago
<span
class="cmr-12">replicated and distributed coarsest-matrix layout; therefore, setting the solver after the</span>
<span
class="cmr-12">layout may change the layout. Similarly, setting the layout after the solver may change</span>
<span
class="cmr-12">the solver.</span>
4 years ago
<!--l. 183--><p class="indent" > <span
4 years ago
class="cmr-12">More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be</span>
<span
class="cmr-12">replicated, while SuperLU</span><span
class="cmr-12">_Dist requires it to be distributed. In these cases, setting the</span>
<span
class="cmr-12">coarsest-level solver implies that the layout is redefined according to the solver,</span>
<span
class="cmr-12">ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel and</span>
<span
class="cmr-12">block-Jacobi can be applied to replicated and distributed matrices, thus their choice</span>
<span
class="cmr-12">does not modify any previously specified layout. It is worth noting that, when the</span>
<span
class="cmr-12">matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi</span>
<span
class="cmr-12">solvers reduce to the corresponding local solver objects (see Remark</span><span
class="cmr-12">&#x00A0;2). For the</span>
<span
class="cmr-12">point-Jacobi and Gauss-Seidel solvers, these objects correspond to a </span><span
class="cmti-12">single</span>
4 years ago
4 years ago
<span
class="cmr-12">point-Jacobi sweep and a </span><span
class="cmti-12">single </span><span
class="cmr-12">Gauss-Seidel sweep, respectively, which are very poor</span>
<span
class="cmr-12">solvers.</span>
4 years ago
<!--l. 198--><p class="indent" > <span
4 years ago
class="cmr-12">On the other hand, the distributed layout can be used with any solver but</span>
<span
class="cmr-12">UMFPACK and SuperLU; therefore, if any of these two solvers has already been</span>
<span
class="cmr-12">selected, the coarsest-level solver is changed to block-Jacobi, with the previously</span>
<span
class="cmr-12">chosen solver applied to the local blocks. Likewise, the replicated layout can be</span>
<span
class="cmr-12">used with any solver but SuperLu</span><span
class="cmr-12">_Dist; therefore, if SuperLu</span><span
class="cmr-12">_Dist has been</span>
<span
class="cmr-12">previously set, the coarsest-level solver is changed to the default sequential</span>
<span
class="cmr-12">solver.</span>
4 years ago
<!--l. 206--><p class="indent" > <span
4 years ago
class="cmbx-12">Remark 4. </span><span
class="cmr-12">The argument </span><span class="lstinline"></span><span
class="cmtt-12">idx</span> <span
4 years ago
class="cmr-12">can be used to allow finer control for those solvers;</span>
<span
class="cmr-12">for instance, by specifying the keyword </span><span class="lstinline"></span><span
class="cmtt-12">&#8217;</span><span
class="cmtt-12">MUMPS_IPAR_ENTRY</span><span
class="cmtt-12">&#8217;</span> <span
4 years ago
class="cmr-12">and an appropriate value</span>
<span
class="cmr-12">for </span><span class="lstinline"></span><span
class="cmtt-12">idx</span><span
4 years ago
class="cmr-12">, it is possible to set any entry in the MUMPS integer control array. See also</span>
<span
class="cmr-12">Sec.</span><span
class="cmr-12">&#x00A0;</span><a
href="userhtmlse6.html#x25-290006"><span
class="cmr-12">6</span><!--tex4ht:ref: sec:adding --></a><span
class="cmr-12">.</span>
<div class="table">
4 years ago
<!--l. 217--><p class="indent" > <a
id="x17-16009r2"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 217--><p class="noindent" >
4 years ago
<div class="tabular"> <table id="TBL-4" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-4-1g"><col
id="TBL-4-1"></colgroup><colgroup id="TBL-4-2g"><col
id="TBL-4-2"></colgroup><colgroup id="TBL-4-3g"><col
id="TBL-4-3"></colgroup><colgroup id="TBL-4-4g"><col
id="TBL-4-4"></colgroup><colgroup id="TBL-4-5g"><col
id="TBL-4-5"></colgroup><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-4-1-"><td style="white-space:wrap; text-align:left;" id="TBL-4-1-1"
4 years ago
class="td11"><!--l. 221--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-4-1-2"
4 years ago
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-4-1-3"
4 years ago
class="td11"><!--l. 221--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-1-4"
4 years ago
class="td11"><!--l. 221--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-1-5"
4 years ago
class="td11"><!--l. 222--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-4-2-"><td style="white-space:wrap; text-align:left;" id="TBL-4-2-1"
4 years ago
class="td11"><!--l. 223--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">ML_CYCLE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-4-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 223--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-3"
4 years ago
class="td11"><!--l. 224--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">VCYCLE</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 224--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">WCYCLE</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 224--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">KCYCLE</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 224--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">ADD</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-4"
4 years ago
class="td11"><!--l. 225--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">VCYCLE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-5"
4 years ago
class="td11"><!--l. 226--><p class="noindent" >Multilevel cycle: V-cycle, W-cycle, K-cycle,
4 years ago
and additive composition. </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-4-3-"><td style="white-space:wrap; text-align:left;" id="TBL-4-3-1"
4 years ago
class="td11"><!--l. 227--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">OUTER_SWEEPS</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-4-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 227--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-3"
4 years ago
class="td11"><!--l. 228--><p class="noindent" >Any integer
<!--l. 228--><p class="noindent" >number <span
class="cmsy-10x-x-109">&#x2265; </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-4"
class="td11"><!--l. 228--><p class="noindent" >1 </td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-5"
4 years ago
class="td11"><!--l. 229--><p class="noindent" >Number of multilevel cycles. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-4-4-"><td style="white-space:wrap; text-align:left;" id="TBL-4-4-1"
4 years ago
class="td11"> </td></tr></table></div></div>
<br /> <div class="caption"
><span class="id">Table&#x00A0;2: </span><span
class="content">Parameters defining the multilevel cycle and the number of cycles to be
applied. </span></div><!--tex4ht:label?: x17-16009r2 -->
4 years ago
</div><hr class="endfloat" />
</div>
<div class="table">
4 years ago
<!--l. 239--><p class="indent" > <a
id="x17-16010r3"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 239--><p class="noindent" >
4 years ago
<div class="tabular"> <table id="TBL-5" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-5-1g"><col
id="TBL-5-1"></colgroup><colgroup id="TBL-5-2g"><col
id="TBL-5-2"></colgroup><colgroup id="TBL-5-3g"><col
id="TBL-5-3"></colgroup><colgroup id="TBL-5-4g"><col
id="TBL-5-4"></colgroup><colgroup id="TBL-5-5g"><col
id="TBL-5-5"></colgroup><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-1-"><td style="white-space:wrap; text-align:left;" id="TBL-5-1-1"
4 years ago
class="td11"><!--l. 243--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-1-2"
4 years ago
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-5-1-3"
4 years ago
class="td11"><!--l. 243--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-1-4"
4 years ago
class="td11"><!--l. 243--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-1-5"
4 years ago
class="td11"><!--l. 244--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
4 years ago
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-2-"><td style="white-space:wrap; text-align:left;" id="TBL-5-2-1"
4 years ago
class="td11"><!--l. 245--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MIN_COARSE_SIZE_PER_PROCESS</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 245--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-3"
4 years ago
class="td11"><!--l. 246--><p class="noindent" >Any number
<!--l. 246--><p class="noindent" ><span
class="cmmi-10x-x-109">&#x003E; </span>0 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-4"
class="td11"><!--l. 247--><p class="noindent" >200 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-5"
4 years ago
class="td11"><!--l. 248--><p class="noindent" >Coarse size threshold per process. The
4 years ago
aggregation stops if the global number of
variables of the computed coarsest matrix
is lower than or equal to this threshold
multiplied by the number of processes.
4 years ago
<!--l. 254--><p class="noindent" > </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-3-"><td style="white-space:wrap; text-align:left;" id="TBL-5-3-1"
4 years ago
class="td11"><!--l. 255--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MIN_COARSE_SIZE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 255--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-3"
4 years ago
class="td11"><!--l. 256--><p class="noindent" >Any number
<!--l. 256--><p class="noindent" ><span
class="cmmi-10x-x-109">&#x003E; </span>0 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-4"
class="td11"><!--l. 257--><p class="noindent" >-1 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-5"
4 years ago
class="td11"><!--l. 258--><p class="noindent" >Coarse size threshold. The aggregation
4 years ago
stops if the global number of variables
of the computed coarsest matrix is lower
than or equal
to this threshold (see Note). If negative,
it is ignored in favour of the default for
<span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MIN_COARSE_SIZE_PER_PROCESS</span><span
class="cmtt-10x-x-109">&#8217;</span>. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-4-"><td style="white-space:wrap; text-align:left;" id="TBL-5-4-1"
4 years ago
class="td11"><!--l. 267--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MIN_CR_RATIO</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-4-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 267--><p class="noindent" ><span
class="cmtt-10x-x-109">real</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-3"
4 years ago
class="td11"><!--l. 268--><p class="noindent" >Any number
<!--l. 268--><p class="noindent" ><span
class="cmmi-10x-x-109">&#x003E; </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-4"
class="td11"><!--l. 269--><p class="noindent" >1.5 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-5"
4 years ago
class="td11"><!--l. 270--><p class="noindent" >Minimum coarsening
4 years ago
ratio. The aggregation stops if the ratio
between the global matrix dimensions at
two consecutive levels is lower than or
equal to this threshold (see Note). </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-5-"><td style="white-space:wrap; text-align:left;" id="TBL-5-5-1"
4 years ago
class="td11"><!--l. 275--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MAX_LEVS</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-5-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 275--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-3"
4 years ago
class="td11"><!--l. 276--><p class="noindent" >Any integer
<!--l. 276--><p class="noindent" >number <span
class="cmmi-10x-x-109">&#x003E; </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-4"
class="td11"><!--l. 277--><p class="noindent" >20 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-5"
4 years ago
class="td11"><!--l. 278--><p class="noindent" >Maximum number of levels. The
4 years ago
aggregation stops if the number of levels
reaches this value (see Note). </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-6-"><td style="white-space:wrap; text-align:left;" id="TBL-5-6-1"
4 years ago
class="td11"><!--l. 280--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">PAR_AGGR_ALG</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-6-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 280--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-3"
4 years ago
class="td11"><!--l. 281--><p class="noindent" ><span
4 years ago
class="cmtt-10x-x-109">&#8217;DEC&#8217;</span>,
<span
class="cmtt-10x-x-109">&#8217;SYMDEC&#8217;</span>,
<span
class="cmtt-10x-x-109">&#8217;COUPLED&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-4"
4 years ago
class="td11"><!--l. 282--><p class="noindent" ><span
class="cmtt-10x-x-109">&#8217;DEC&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-5"
4 years ago
class="td11"><!--l. 283--><p class="noindent" >Parallel aggregation algorithm.
<!--l. 283--><p class="noindent" >the <span class="lstinline"></span><span
class="cmtt-10x-x-109">SYMDEC</span> option applies decoupled
4 years ago
aggregation to the sparsity pattern of
<span
class="cmmi-10x-x-109">A </span>+ <span
class="cmmi-10x-x-109">A</span><sup><span
class="cmmi-8">T</span> </sup>. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-7-"><td style="white-space:wrap; text-align:left;" id="TBL-5-7-1"
4 years ago
class="td11"><!--l. 297--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-7-2"
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-3"
4 years ago
class="td11"><!--l. 297--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-4"
4 years ago
class="td11"><!--l. 297--><p class="noindent" ><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-5"
4 years ago
class="td11"><!--l. 298--><p class="noindent" ><span
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-8-"><td style="white-space:wrap; text-align:left;" id="TBL-5-8-1"
4 years ago
class="td11"><!--l. 299--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_TYPE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-8-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 299--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-8-3"
4 years ago
class="td11"><!--l. 300--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SOC1</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-8-4"
4 years ago
class="td11"><!--l. 301--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SOC1</span><span
class="cmtt-10x-x-109">&#8217;</span>,
<span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SOC2</span><span
class="cmtt-10x-x-109">&#8217;</span>,
<span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MATCHBOXP</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-8-5"
4 years ago
class="td11"><!--l. 304--><p class="noindent" >Type of aggregation algorithm: currently,
4 years ago
for the
decoupled aggregation we implement two
measures of strength of connection, the
one by Van&#x011B;k, Mandel and Brezina&#x00A0;<span class="cite">[<a
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">30</a>]</span>,
4 years ago
and the one by Gratton et al&#x00A0;<span class="cite">[<a
href="userhtmlli4.html#XGrHeJi:16">20</a>]</span>. The
4 years ago
coupled aggregation is based on a parallel
version of the half-approximate matching
implemented in the MatchBox-P software
package&#x00A0;<span class="cite">[<a
href="userhtmlli4.html#XMatchBoxP">8</a>]</span>. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-9-"><td style="white-space:wrap; text-align:left;" id="TBL-5-9-1"
4 years ago
class="td11"><!--l. 312--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_SIZE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-9-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 312--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-9-3"
4 years ago
class="td11"><!--l. 313--><p class="noindent" >Any integer
<!--l. 313--><p class="noindent" >number
4 years ago
power of 2
and <span
class="cmmi-10x-x-109">&#x003E; </span>2 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-9-4"
class="td11"><!--l. 314--><p class="noindent" >4 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-9-5"
4 years ago
class="td11"><!--l. 315--><p class="noindent" >Maximum size of aggregates when the
4 years ago
coupled aggregation based on matching
is applied. For aggressive coarsening
with size of aggregate larger than 8
we recommend the use of smoothed
prolongators. <span
class="cmbx-10x-x-109">MODIFICARE</span>
<span
class="cmbx-10x-x-109">CODICE</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-10-"><td style="white-space:wrap; text-align:left;" id="TBL-5-10-1"
4 years ago
class="td11"><!--l. 320--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_PROL</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-10-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 320--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-10-3"
4 years ago
class="td11"><!--l. 321--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SMOOTHED</span><span
class="cmtt-10x-x-109">&#8217;</span>,
<span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">UNSMOOTHED</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-10-4"
4 years ago
class="td11"><!--l. 321--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SMOOTHED</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-10-5"
4 years ago
class="td11"><!--l. 322--><p class="noindent" >Prolongator used by the aggregation
4 years ago
algorithm: smoothed or unsmoothed (i.e.,
tentative prolongator). </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-11-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-11-1"
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;"><span
class="cmbx-10x-x-109">Note. </span>The aggregation algorithm stops when at least one of the following criteria is met: the coarse size threshold, </div>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-5-12-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-12-1"
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">the coarse size threshold per process, the minimum coarsening ratio, or the maximum number of levels is reached.</div>
</tr><tr
style="vertical-align:baseline;" id="TBL-5-13-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-13-1"
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">Therefore, the actual number of levels may be smaller than the specified maximum number of levels. </div>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-5-14-"><td style="white-space:wrap; text-align:left;" id="TBL-5-14-1"
4 years ago
class="td11"> </td></tr></table>
</div>
4 years ago
<br /> <div class="caption"
><span class="id">Table&#x00A0;3: </span><span
class="content">Parameters defining the aggregation algorithm. </span></div><!--tex4ht:label?: x17-16010r3 -->
</div>
4 years ago
</div><hr class="endfloat" />
</div>
<div class="table">
4 years ago
<!--l. 340--><p class="indent" > <a
id="x17-16011r4"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 340--><p class="noindent" >
4 years ago
<div class="tabular"> <table id="TBL-6" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-6-1g"><col
id="TBL-6-1"></colgroup><colgroup id="TBL-6-2g"><col
id="TBL-6-2"></colgroup><colgroup id="TBL-6-3g"><col
id="TBL-6-3"></colgroup><colgroup id="TBL-6-4g"><col
id="TBL-6-4"></colgroup><colgroup id="TBL-6-5g"><col
id="TBL-6-5"></colgroup><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-1-"><td style="white-space:wrap; text-align:left;" id="TBL-6-1-1"
4 years ago
class="td11"><!--l. 344--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-1-2"
4 years ago
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-6-1-3"
4 years ago
class="td11"><!--l. 344--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-1-4"
4 years ago
class="td11"><!--l. 344--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-1-5"
4 years ago
class="td11"><!--l. 345--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-2-"><td style="white-space:wrap; text-align:left;" id="TBL-6-2-1"
4 years ago
class="td11"><!--l. 347--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_ORD</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 347--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-3"
4 years ago
class="td11"><!--l. 348--><p class="noindent" ><span
4 years ago
class="cmtt-10x-x-109">&#8217;NATURAL&#8217;</span>
4 years ago
<!--l. 348--><p class="noindent" ><span
class="cmtt-10x-x-109">&#8217;DEGREE&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-4"
4 years ago
class="td11"><!--l. 349--><p class="noindent" ><span
class="cmtt-10x-x-109">&#8217;NATURAL&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-5"
4 years ago
class="td11"><!--l. 350--><p class="noindent" >Initial ordering of indices for
4 years ago
the decoupled aggregation algorithm:
either natural ordering or sorted by
descending degrees of the nodes in the
matrix graph. </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-3-"><td style="white-space:wrap; text-align:left;" id="TBL-6-3-1"
4 years ago
class="td11"><!--l. 357--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_THRESH</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 357--><p class="noindent" ><span
class="cmtt-10x-x-109">real</span><span
class="cmtt-10x-x-109">(</span> <span
4 years ago
class="cmti-10x-x-109">kind</span><span
4 years ago
class="cmti-10x-x-109">_parameter</span><span class="lstinline"></span><!--l. 357--><p class="noindent" ><span
class="cmtt-10x-x-109">)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-3"
4 years ago
class="td11"><!--l. 358--><p class="noindent" >Any&#x00A0;real
<!--l. 358--><p class="noindent" >number&#x00A0;<span
4 years ago
class="cmsy-10x-x-109">&#x2208;</span>
[0<span
class="cmmi-10x-x-109">,</span>1] </td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-4"
class="td11"><!--l. 359--><p class="noindent" >0.01 </td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-5"
4 years ago
class="td11"><!--l. 360--><p class="noindent" >The threshold <span
4 years ago
class="cmmi-10x-x-109">&#x03B8; </span>in the decoupled
aggregation algorithm, see (<span
class="cmbx-10x-x-109">??</span>) in
Section&#x00A0;<span
class="cmbx-10x-x-109">??</span>. See also the note at the
bottom of this table. </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-4-"><td style="white-space:wrap; text-align:left;" id="TBL-6-4-1"
4 years ago
class="td11"><!--l. 363--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AGGR_FILTER</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 364--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-3"
4 years ago
class="td11"><!--l. 365--><p class="noindent" ><span
4 years ago
class="cmtt-10x-x-109">&#8217;FILTER&#8217;</span>
4 years ago
<!--l. 365--><p class="noindent" ><span
class="cmtt-10x-x-109">&#8217;NOFILTER&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-4"
4 years ago
class="td11"><!--l. 366--><p class="noindent" ><span
class="cmtt-10x-x-109">&#8217;NOFILTER&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-5"
4 years ago
class="td11"><!--l. 366--><p class="noindent" >Matrix used in computing the smoothed
4 years ago
prolongator: filtered or unfiltered
(see&#x00A0;(<span
class="cmbx-10x-x-109">??</span>) in Section&#x00A0;<span
class="cmbx-10x-x-109">??</span>). </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-5-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-6-5-1"
4 years ago
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;"><span
class="cmbx-10x-x-109">Note. </span>Different thresholds at different levels, such as those used in <span class="cite">[<a
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">30</a>, Section&#x00A0;5.1]</span>, can be easily set by invoking the rou-</div>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-6-6-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-6-6-1"
4 years ago
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">tine <span
class="cmtt-10x-x-109">set </span>with the parameter <span
class="cmtt-10x-x-109">ilev</span>.</div>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-6-7-"><td style="white-space:wrap; text-align:left;" id="TBL-6-7-1"
4 years ago
class="td11"> </td></tr></table></div></div>
<br /> <div class="caption"
><span class="id">Table&#x00A0;4: </span><span
class="content">Parameters defining the aggregation algorithm (continued). </span></div><!--tex4ht:label?: x17-16011r4 -->
4 years ago
</div><hr class="endfloat" />
</div>
<div class="table">
4 years ago
<!--l. 382--><p class="indent" > <a
id="x17-16012r5"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 382--><p class="noindent" >
4 years ago
<div class="tabular"> <table id="TBL-7" class="tabular"
cellspacing="0" cellpadding="0"
><colgroup id="TBL-7-1g"><col
id="TBL-7-1"></colgroup><colgroup id="TBL-7-2g"><col
id="TBL-7-2"></colgroup><colgroup id="TBL-7-3g"><col
id="TBL-7-3"></colgroup><colgroup id="TBL-7-4g"><col
id="TBL-7-4"></colgroup><colgroup id="TBL-7-5g"><col
id="TBL-7-5"></colgroup><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-1-"><td style="white-space:wrap; text-align:left;" id="TBL-7-1-1"
4 years ago
class="td11"><!--l. 385--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-1-2"
4 years ago
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-7-1-3"
4 years ago
class="td11"><!--l. 385--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-1-4"
4 years ago
class="td11"><!--l. 385--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-1-5"
4 years ago
class="td11"><!--l. 386--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-2-"><td style="white-space:wrap; text-align:left;" id="TBL-7-2-1"
4 years ago
class="td11"><!--l. 387--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_MAT</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 387--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-3"
4 years ago
class="td11"><!--l. 388--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">DIST</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 388--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">REPL</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-4"
4 years ago
class="td11"><!--l. 389--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">REPL</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-5"
4 years ago
class="td11"><!--l. 390--><p class="noindent" >Coarsest matrix layout: distributed among the
4 years ago
processes or replicated on each of them. </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-3-"><td style="white-space:wrap; text-align:left;" id="TBL-7-3-1"
4 years ago
class="td11"><!--l. 392--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_SOLVE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 392--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-3"
4 years ago
class="td11"><!--l. 393--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MUMPS</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 393--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">UMF</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 394--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SLU</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 394--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SLUDIST</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 395--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">JACOBI</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 395--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">GS</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 395--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">BJAC</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 395--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">RKR</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-4"
class="td11"><!--l. 396--><p class="noindent" >See&#x00A0;Note.</td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-5"
4 years ago
class="td11"><!--l. 397--><p class="noindent" >Solver used at the coarsest level: sequential LU
4 years ago
from MUMPS, UMFPACK, or SuperLU (plus
triangular solve); distributed LU from MUMPS or
SuperLU_Dist (plus triangular solve); point-Jacobi,
hybrid Gauss-Seidel or block-Jacobi and related
<span
4 years ago
class="cmmi-10x-x-109">&#x2113;</span><sub><span
class="cmr-8">1</span></sub>-versions;
<span
4 years ago
class="cmbx-10x-x-109">preconditioned Conjugate Gradient coupled</span>
<span
4 years ago
class="cmbx-10x-x-109">with the block-Jacobi preconditioner with</span>
<span
class="cmbx-10x-x-109">ILU(0) on the blocks</span>. Note that <span
class="cmtt-10x-x-109">UMF </span>and
<span
class="cmtt-10x-x-109">SLU </span>require the coarsest matrix to be replicated,
<span
4 years ago
class="cmtt-10x-x-109">SLUDIST</span>, <span
class="cmtt-10x-x-109">JACOBI</span>, <span
class="cmtt-10x-x-109">GS</span>, <span
class="cmtt-10x-x-109">BJAC </span>and <span
class="cmtt-10x-x-109">PCG </span>require it to
be distributed, <span
class="cmtt-10x-x-109">MUMPS </span>can be used with either a
replicated or a distributed matrix. When any of
the previous solvers is specified, the matrix layout
is set to a default value which allows the use of
the solver (see Remark 3, p.&#x00A0;24). Note also that
4 years ago
UMFPACK and SuperLU_Dist are available only in
double precision. </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-4-"><td style="white-space:wrap; text-align:left;" id="TBL-7-4-1"
4 years ago
class="td11"><!--l. 424--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_SUBSOLVE</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-4-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 424--><p class="noindent" ><span
class="cmtt-10x-x-109">character</span><span
class="cmtt-10x-x-109">(</span><span
class="cmtt-10x-x-109">len</span><span
class="cmtt-10x-x-109">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-3"
4 years ago
class="td11"><!--l. 425--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">ILU</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 425--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">ILUT</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 425--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MILU</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 426--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">MUMPS</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 426--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">SLU</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 426--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">UMF</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 427--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">INVT</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 427--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">INVK</span><span
class="cmtt-10x-x-109">&#8217;</span>
4 years ago
<!--l. 427--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">AINV</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-4"
class="td11"><!--l. 428--><p class="noindent" >See&#x00A0;Note.</td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-5"
4 years ago
class="td11"><!--l. 429--><p class="noindent" >Solver for the diagonal blocks of the coarse matrix,
4 years ago
in case the block Jacobi solver is chosen as
coarsest-level solver: ILU(<span
class="cmmi-10x-x-109">p</span>), ILU(<span
class="cmmi-10x-x-109">p,t</span>), MILU(<span
class="cmmi-10x-x-109">p</span>),
LU from MUMPS, SuperLU or UMFPACK (plus
triangular solve). Suitable for GPUs (no triangular
solve) approximate inverse solvers INVK(<span
class="cmmi-10x-x-109">p,q</span>),
INVT(<span
class="cmmi-10x-x-109">p</span><sub><span
class="cmr-8">1</span></sub><span
class="cmmi-10x-x-109">,p</span>2<span
class="cmmi-10x-x-109">,t</span><sub><span
class="cmr-8">1</span></sub><span
class="cmmi-10x-x-109">,t</span><sub><span
class="cmr-8">2</span></sub>) and AINV(<span
class="cmmi-10x-x-109">t</span>), see&#x00A0;<span class="cite">[<a
href="userhtmlli4.html#XBERTACCINIFILIPPONE">2</a>]</span>. Note that
UMFPACK and SuperLU_Dist are available only in
double precision. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-5-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-7-5-1"
4 years ago
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;"><span
class="cmbx-10x-x-109">Note. </span>Defaults for <span
class="cmtt-10x-x-109">COARSE</span><span
class="cmtt-10x-x-109">_SOLVE </span>and <span
class="cmtt-10x-x-109">COARSE</span><span
class="cmtt-10x-x-109">_SUBSOLVE </span>are chosen in the following order:</div>
</tr><tr
style="vertical-align:baseline;" id="TBL-7-6-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-7-6-1"
4 years ago
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">single precision version &#8211; <span
class="cmtt-10x-x-109">MUMPS </span>if installed, then <span
class="cmtt-10x-x-109">SLU </span>if installed, <span
class="cmtt-10x-x-109">ILU </span>otherwise;</div>
</tr><tr
style="vertical-align:baseline;" id="TBL-7-7-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-7-7-1"
4 years ago
class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">double precision version &#8211; <span
class="cmtt-10x-x-109">UMF </span>if installed, then <span
class="cmtt-10x-x-109">MUMPS </span>if installed, then <span
class="cmtt-10x-x-109">SLU </span>if installed, <span
class="cmtt-10x-x-109">ILU </span>otherwise.</div>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-8-"><td style="white-space:wrap; text-align:left;" id="TBL-7-8-1"
4 years ago
class="td11"><!--l. 458--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-8-2"
4 years ago
class="td11"><span
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-7-8-3"
4 years ago
class="td11"><!--l. 458--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-8-4"
4 years ago
class="td11"><!--l. 458--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-8-5"
4 years ago
class="td11"><!--l. 459--><p class="noindent" ><span
4 years ago
class="cmcsc-10x-x-109"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td>
</tr><tr
4 years ago
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-9-"><td style="white-space:wrap; text-align:left;" id="TBL-7-9-1"
4 years ago
class="td11"><!--l. 460--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_SWEEPS</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-9-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 460--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-9-3"
4 years ago
class="td11"><!--l. 461--><p class="noindent" >Any
integer
4 years ago
<!--l. 461--><p class="noindent" >number <span
class="cmmi-10x-x-109">&#x003E;</span>
0 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-9-4"
class="td11"><!--l. 462--><p class="noindent" >10 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-9-5"
4 years ago
class="td11"><!--l. 463--><p class="noindent" >Number of sweeps when <span class="lstinline"></span><span
class="cmtt-10x-x-109">JACOBI</span>, <span class="lstinline"></span><span
class="cmtt-10x-x-109">GS</span> or <span class="lstinline"></span><span
class="cmtt-10x-x-109">BJAC</span>
is chosen as coarsest-level solver. <span
4 years ago
class="cmbx-10x-x-109">Aggiungere</span>
<span
class="cmbx-10x-x-109">criterio di arresto del PCG?</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-10-"><td style="white-space:wrap; text-align:left;" id="TBL-7-10-1"
4 years ago
class="td11"><!--l. 465--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_FILLIN</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-10-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 465--><p class="noindent" ><span
class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-10-3"
4 years ago
class="td11"><!--l. 466--><p class="noindent" >Any
integer
4 years ago
<!--l. 466--><p class="noindent" >number <span
class="cmsy-10x-x-109">&#x2265;</span>
0 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-10-4"
class="td11"><!--l. 467--><p class="noindent" >0 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-10-5"
4 years ago
class="td11"><!--l. 468--><p class="noindent" >Fill-in level <span
class="cmmi-10x-x-109">p </span>of the ILU factorizations. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-11-"><td style="white-space:wrap; text-align:left;" id="TBL-7-11-1"
4 years ago
class="td11"><!--l. 469--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10x-x-109">&#8217;</span><span
class="cmtt-10x-x-109">COARSE_ILUTHRS</span><span
class="cmtt-10x-x-109">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-11-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 470--><p class="noindent" ><span
class="cmtt-10x-x-109">real</span><span
class="cmtt-10x-x-109">(</span> <span
4 years ago
class="cmti-10x-x-109">kind</span><span
4 years ago
class="cmti-10x-x-109">_parameter</span><span class="lstinline"></span><!--l. 470--><p class="noindent" ><span
class="cmtt-10x-x-109">)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-11-3"
4 years ago
class="td11"><!--l. 471--><p class="noindent" >Any real
<!--l. 471--><p class="noindent" >number <span
class="cmsy-10x-x-109">&#x2265;</span>
0 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-11-4"
class="td11"><!--l. 472--><p class="noindent" >0 </td><td style="white-space:wrap; text-align:left;" id="TBL-7-11-5"
4 years ago
class="td11"><!--l. 473--><p class="noindent" >Drop tolerance <span
class="cmmi-10x-x-109">t </span>in the ILU(<span
class="cmmi-10x-x-109">p,t</span>) factorization. </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-7-12-"><td style="white-space:wrap; text-align:left;" id="TBL-7-12-1"
class="td11"> </td></tr></table>
</div></div>
4 years ago
<br /> <div class="caption"
><span class="id">Table&#x00A0;5: </span><span
4 years ago
class="content">Parameters defining the coarse-space correction at the coarsest level
(continued).</span></div><!--tex4ht:label?: x17-16012r5 -->
4 years ago
</div><hr class="endfloat" />
</div>
<div class="table">
4 years ago
<!--l. 482--><p class="indent" > <a
id="x17-16013r6"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 482--><p class="noindent" >
<div class="tabular"> <table id="TBL-8" class="tabular"
4 years ago
cellspacing="0" cellpadding="0"
><colgroup id="TBL-8-1g"><col
id="TBL-8-1"></colgroup><colgroup id="TBL-8-2g"><col
id="TBL-8-2"></colgroup><colgroup id="TBL-8-3g"><col
id="TBL-8-3"></colgroup><colgroup id="TBL-8-4g"><col
id="TBL-8-4"></colgroup><colgroup id="TBL-8-5g"><col
id="TBL-8-5"></colgroup><tr
4 years ago
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-1-"><td style="white-space:wrap; text-align:left;" id="TBL-8-1-1"
4 years ago
class="td11"><!--l. 486--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-1-2"
4 years ago
class="td11"><span
class="cmcsc-10"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-8-1-3"
4 years ago
class="td11"><!--l. 486--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-1-4"
4 years ago
class="td11"><!--l. 486--><p class="noindent" ><span
4 years ago
class="cmcsc-10"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-1-5"
4 years ago
class="td11"><!--l. 487--><p class="noindent" ><span
4 years ago
class="cmcsc-10"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-2-"><td style="white-space:wrap; text-align:left;" id="TBL-8-2-1"
4 years ago
class="td11"><!--l. 489--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SMOOTHER_TYPE</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 489--><p class="noindent" ><span
class="cmtt-10">character</span><span
class="cmtt-10">(</span><span
class="cmtt-10">len</span><span
class="cmtt-10">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-3"
4 years ago
class="td11"><!--l. 490--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">JACOBI</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 490--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">GS</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 490--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">BGS</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 490--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">BJAC</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 491--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">AS</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-4"
4 years ago
class="td11"><!--l. 492--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">FBGS</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-5"
4 years ago
class="td11"><!--l. 493--><p class="noindent" ><span
4 years ago
class="cmr-10">Type of smoother used in the multilevel</span>
<span
class="cmr-10">preconditioner: point-Jacobi, hybrid</span>
<span
class="cmr-10">(forward) Gauss-Seidel, hybrid backward</span>
<span
class="cmr-10">Gauss-Seidel, block-Jacobi, </span><span
class="cmmi-10">&#x2113;</span><sub><span
class="cmr-7">1</span></sub><span
class="cmbx-10">-versions?</span>
<span
class="cmr-10">and Additive Schwarz.</span>
4 years ago
<!--l. 497--><p class="noindent" ><span
4 years ago
class="cmr-10">It is ignored by one-level preconditioners.</span> </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-3-"><td style="white-space:wrap; text-align:left;" id="TBL-8-3-1"
4 years ago
class="td11"><!--l. 498--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_SOLVE</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 498--><p class="noindent" ><span
class="cmtt-10">character</span><span
class="cmtt-10">(</span><span
class="cmtt-10">len</span><span
class="cmtt-10">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-3"
4 years ago
class="td11"><!--l. 499--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">JACOBI</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 500--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">GS</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 500--><p class="noindent" ><span
4 years ago
class="cmtt-10">&#8217;BGS&#8217;</span>
4 years ago
<!--l. 500--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">ILU</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 501--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">ILUT</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 501--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">MILU</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 502--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">MUMPS</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 502--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SLU</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 502--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">UMF</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-4"
4 years ago
class="td11"><!--l. 503--><p class="noindent" ><span
4 years ago
class="cmtt-10">GS </span><span
class="cmr-10">and </span><span
class="cmtt-10">BGS </span><span
class="cmr-10">for pre-</span>
<span
class="cmr-10">and post-smoothers of</span>
<span
class="cmr-10">multilevel</span>
<span
class="cmr-10">preconditioners,</span>
<span
class="cmr-10">respectively</span>
4 years ago
<!--l. 505--><p class="noindent" ><span
4 years ago
class="cmtt-10">ILU </span><span
class="cmr-10">for block-Jacobi</span>
<span
class="cmr-10">and Additive Schwarz</span>
<span
class="cmr-10">one-level</span>
<span
class="cmr-10">preconditioners</span>
<span
class="cmmi-10">&#x2113;</span><sub><span
class="cmr-7">1</span></sub><span
class="cmbx-10">-versions?</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-5"
4 years ago
class="td11"><!--l. 508--><p class="noindent" ><span
4 years ago
class="cmr-10">The local solver to be used with the</span>
<span
class="cmr-10">smoother or one-level preconditioner (see</span>
<span
class="cmr-10">Remark</span><span
class="cmr-10">&#x00A0;2, page</span><span
class="cmr-10">&#x00A0;24): point-Jacobi, hybrid</span>
<span
class="cmr-10">(forward) Gauss-Seidel, hybrid backward</span>
<span
class="cmr-10">Gauss-Seidel, ILU(</span><span
class="cmmi-10">p</span><span
class="cmr-10">), ILU(</span><span
class="cmmi-10">p,t</span><span
class="cmr-10">), MILU(</span><span
class="cmmi-10">p</span><span
class="cmr-10">),</span>
<span
class="cmr-10">LU from MUMPS, SuperLU</span>
<span
class="cmr-10">or UMFPACK (plus triangular solve). See</span>
<span
class="cmr-10">Note for details on hybrid Gauss-Seidel.</span> </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-4-"><td style="white-space:wrap; text-align:left;" id="TBL-8-4-1"
4 years ago
class="td11"><!--l. 515--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SMOOTHER_SWEEPS</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 515--><p class="noindent" ><span
class="cmtt-10">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-3"
4 years ago
class="td11"><!--l. 516--><p class="noindent" ><span
4 years ago
class="cmr-10">Any integer</span>
4 years ago
<!--l. 516--><p class="noindent" ><span
4 years ago
class="cmr-10">number</span><span
class="cmr-10">&#x00A0;</span><span
class="cmsy-10">&#x2265; </span><span
class="cmr-10">0</span></td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-4"
4 years ago
class="td11"><!--l. 517--><p class="noindent" ><span
class="cmr-10">1</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-5"
4 years ago
class="td11"><!--l. 518--><p class="noindent" ><span
4 years ago
class="cmr-10">Number of sweeps of the smoother or</span>
<span
class="cmr-10">one-level preconditioner. In the multilevel</span>
<span
class="cmr-10">case, no pre-smother or post-smoother</span>
<span
class="cmr-10">is used if this parameter is set to 0</span>
<span
class="cmr-10">together with </span><span class="lstinline"></span><span
class="cmtt-10">pos</span><span
class="cmtt-10">=</span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">PRE</span><span
class="cmtt-10">&#8217;</span> <span
class="cmr-10">or </span><span class="lstinline"></span><span
class="cmtt-10">pos</span><span
class="cmtt-10">=</span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">POST</span><span
4 years ago
class="cmr-10">,</span>
<span
class="cmr-10">respectively.</span> </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-5-"><td style="white-space:wrap; text-align:left;" id="TBL-8-5-1"
4 years ago
class="td11"><!--l. 523--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_OVR</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-5-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 523--><p class="noindent" ><span
class="cmtt-10">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-3"
4 years ago
class="td11"><!--l. 524--><p class="noindent" ><span
4 years ago
class="cmr-10">Any integer</span>
4 years ago
<!--l. 524--><p class="noindent" ><span
4 years ago
class="cmr-10">number</span><span
class="cmr-10">&#x00A0;</span><span
class="cmsy-10">&#x2265; </span><span
class="cmr-10">0</span></td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-4"
4 years ago
class="td11"><!--l. 525--><p class="noindent" ><span
class="cmr-10">1</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-5"
4 years ago
class="td11"><!--l. 526--><p class="noindent" ><span
4 years ago
class="cmr-10">Number of overlap layers, for Additive</span>
<span
class="cmr-10">Schwarz only.</span> </td>
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-8-6-"><td style="white-space:wrap; text-align:left;" id="TBL-8-6-1"
4 years ago
class="td11"> </td></tr></table></div></div>
<br /> <div class="caption"
><span class="id">Table&#x00A0;6: </span><span
4 years ago
class="content">Parameters defining the smoother or the details of the one-level
preconditioner. </span></div><!--tex4ht:label?: x17-16013r6 -->
4 years ago
</div><hr class="endfloat" />
</div>
<div class="table">
4 years ago
<!--l. 535--><p class="indent" > <a
id="x17-16014r7"></a><hr class="float"><div class="float"
4 years ago
>
<div class="center"
>
4 years ago
<!--l. 535--><p class="noindent" >
<div class="tabular"> <table id="TBL-9" class="tabular"
4 years ago
cellspacing="0" cellpadding="0"
><colgroup id="TBL-9-1g"><col
id="TBL-9-1"></colgroup><colgroup id="TBL-9-2g"><col
id="TBL-9-2"></colgroup><colgroup id="TBL-9-3g"><col
id="TBL-9-3"></colgroup><colgroup id="TBL-9-4g"><col
id="TBL-9-4"></colgroup><colgroup id="TBL-9-5g"><col
id="TBL-9-5"></colgroup><tr
4 years ago
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-1-"><td style="white-space:wrap; text-align:left;" id="TBL-9-1-1"
4 years ago
class="td11"><!--l. 539--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">what</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-1-2"
4 years ago
class="td11"><span
class="cmcsc-10"><span
class="small-caps">d</span><span
class="small-caps">a</span><span
class="small-caps">t</span><span
class="small-caps">a</span> <span
class="small-caps">t</span><span
class="small-caps">y</span><span
class="small-caps">p</span><span
class="small-caps">e</span> </span></td><td style="white-space:wrap; text-align:left;" id="TBL-9-1-3"
4 years ago
class="td11"><!--l. 539--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">val</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-1-4"
4 years ago
class="td11"><!--l. 539--><p class="noindent" ><span
4 years ago
class="cmcsc-10"><span
class="small-caps">d</span><span
class="small-caps">e</span><span
class="small-caps">f</span><span
class="small-caps">a</span><span
class="small-caps">u</span><span
class="small-caps">l</span><span
class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-1-5"
4 years ago
class="td11"><!--l. 540--><p class="noindent" ><span
4 years ago
class="cmcsc-10"><span
class="small-caps">c</span><span
class="small-caps">o</span><span
class="small-caps">m</span><span
class="small-caps">m</span><span
class="small-caps">e</span><span
class="small-caps">n</span><span
class="small-caps">t</span><span
class="small-caps">s</span></span> </td></tr><tr
4 years ago
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-2-"><td style="white-space:wrap; text-align:left;" id="TBL-9-2-1"
4 years ago
class="td11"><!--l. 541--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_RESTR</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-2-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 541--><p class="noindent" ><span
class="cmtt-10">character</span><span
class="cmtt-10">(</span><span
class="cmtt-10">len</span><span
class="cmtt-10">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-3"
4 years ago
class="td11"><!--l. 542--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">HALO</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 542--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-4"
4 years ago
class="td11"><!--l. 543--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">HALO</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-5"
4 years ago
class="td11"><!--l. 544--><p class="noindent" ><span
4 years ago
class="cmr-10">Type of restriction operator, for Additive</span>
<span
class="cmr-10">Schwarz only: </span><span
class="cmtt-10">HALO </span><span
class="cmr-10">for taking into account</span>
4 years ago
<span
class="cmr-10">the overlap, </span><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> <span
4 years ago
class="cmr-10">for neglecting it.</span>
4 years ago
<!--l. 547--><p class="noindent" ><span
class="cmr-10">Note that </span><span
4 years ago
class="cmtt-10">HALO </span><span
class="cmr-10">must be chosen for the</span>
4 years ago
<span
class="cmr-10">classical Addditive Schwarz smoother and</span>
4 years ago
<span
class="cmr-10">its RAS variant.</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-3-"><td style="white-space:wrap; text-align:left;" id="TBL-9-3-1"
4 years ago
class="td11"><!--l. 549--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_PROL</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-3-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 549--><p class="noindent" ><span
class="cmtt-10">character</span><span
class="cmtt-10">(</span><span
class="cmtt-10">len</span><span
class="cmtt-10">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-3-3"
4 years ago
class="td11"><!--l. 550--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUM</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 550--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-3-4"
4 years ago
class="td11"><!--l. 551--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-3-5"
4 years ago
class="td11"><!--l. 552--><p class="noindent" ><span
class="cmr-10">Type of prolongation operator, for Additive</span>
4 years ago
<span
class="cmr-10">Schwarz only: </span><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUM</span><span
class="cmtt-10">&#8217;</span> <span
class="cmr-10">for adding the</span>
4 years ago
<span
class="cmr-10">contributions from the overlap, </span><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> <span
class="cmr-10">for</span>
4 years ago
<span
class="cmr-10">neglecting them.</span>
4 years ago
<!--l. 555--><p class="noindent" ><span
class="cmr-10">Note that </span><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUM</span><span
class="cmtt-10">&#8217;</span> <span
class="cmr-10">must be chosen for the</span>
<span
class="cmr-10">classical Additive Schwarz smoother, and</span>
<span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">NONE</span><span
class="cmtt-10">&#8217;</span> <span
class="cmr-10">for its RAS variant.</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-4-"><td style="white-space:wrap; text-align:left;" id="TBL-9-4-1"
4 years ago
class="td11"><!--l. 557--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_FILLIN</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-4-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 557--><p class="noindent" ><span
class="cmtt-10">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-3"
4 years ago
class="td11"><!--l. 558--><p class="noindent" ><span
4 years ago
class="cmr-10">Any integer</span>
4 years ago
<!--l. 558--><p class="noindent" ><span
4 years ago
class="cmr-10">number</span><span
class="cmr-10">&#x00A0;</span><span
class="cmsy-10">&#x2265; </span><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-4"
4 years ago
class="td11"><!--l. 559--><p class="noindent" ><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-5"
4 years ago
class="td11"><!--l. 560--><p class="noindent" ><span
4 years ago
class="cmr-10">Fill-in level </span><span
class="cmmi-10">p </span><span
4 years ago
class="cmr-10">of the incomplete LU</span>
<span
class="cmr-10">factorizations.</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-5-"><td style="white-space:wrap; text-align:left;" id="TBL-9-5-1"
4 years ago
class="td11"><!--l. 561--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">SUB_ILUTHRS</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-5-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 561--><p class="noindent" ><span
class="cmtt-10">real</span><span
class="cmtt-10">(</span> <span
4 years ago
class="cmti-10">kind</span><span
4 years ago
class="cmti-10">_parameter</span><span class="lstinline"></span><!--l. 561--><p class="noindent" ><span
class="cmtt-10">)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-3"
4 years ago
class="td11"><!--l. 562--><p class="noindent" ><span
class="cmr-10">Any real</span>
4 years ago
<span
class="cmr-10">number</span><span
class="cmr-10">&#x00A0;</span><span
class="cmsy-10">&#x2265; </span><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-4"
4 years ago
class="td11"><!--l. 563--><p class="noindent" ><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-5"
4 years ago
class="td11"><!--l. 564--><p class="noindent" ><span
class="cmr-10">Drop tolerance </span><span
class="cmmi-10">t </span><span
class="cmr-10">in the ILU(</span><span
4 years ago
class="cmmi-10">p,t</span><span
class="cmr-10">)</span>
<span
class="cmr-10">factorization.</span> </td>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-9-6-"><td style="white-space:wrap; text-align:left;" id="TBL-9-6-1"
4 years ago
class="td11"><!--l. 565--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">MUMPS_LOC_GLOB</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-6-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 565--><p class="noindent" ><span
class="cmtt-10">character</span><span
class="cmtt-10">(</span><span
class="cmtt-10">len</span><span
class="cmtt-10">=*)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-6-3"
4 years ago
class="td11"><!--l. 566--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">LOCAL_SOLVER</span><span
class="cmtt-10">&#8217;</span>
4 years ago
<!--l. 566--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">GLOBAL_SOLVER</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-6-4"
4 years ago
class="td11"><!--l. 567--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">GLOBAL_SOLVER</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-6-5"
4 years ago
class="td11"><!--l. 568--><p class="noindent" ><span
class="cmr-10">Whether MUMPS should be used as a</span>
4 years ago
<span
class="cmr-10">distributed solver, or as a serial solver acting</span>
<span
class="cmr-10">only on the part of the matrix local to each</span>
<span
class="cmr-10">process.</span> </td>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-9-7-"><td style="white-space:wrap; text-align:left;" id="TBL-9-7-1"
4 years ago
class="td11"><!--l. 572--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">MUMPS_IPAR_ENTRY</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-7-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 572--><p class="noindent" ><span
class="cmtt-10">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-7-3"
4 years ago
class="td11"><!--l. 573--><p class="noindent" ><span
class="cmr-10">Any integer</span>
4 years ago
<span
class="cmr-10">number</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-7-4"
4 years ago
class="td11"><!--l. 574--><p class="noindent" ><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-7-5"
4 years ago
class="td11"><!--l. 575--><p class="noindent" ><span
4 years ago
class="cmr-10">Set an entry in the MUMPS integer control</span>
<span
class="cmr-10">array, as chosen via the </span><span class="lstinline"></span><span
class="cmtt-10">idx</span> <span
class="cmr-10">optional</span>
4 years ago
<span
class="cmr-10">argument.</span> </td>
4 years ago
</tr><tr
style="vertical-align:baseline;" id="TBL-9-8-"><td style="white-space:wrap; text-align:left;" id="TBL-9-8-1"
4 years ago
class="td11"><!--l. 577--><p class="noindent" ><span class="lstinline"></span><span
class="cmtt-10">&#8217;</span><span
class="cmtt-10">MUMPS_RPAR_ENTRY</span><span
class="cmtt-10">&#8217;</span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-8-2"
4 years ago
class="td11"><span class="lstinline"></span><!--l. 577--><p class="noindent" ><span
class="cmtt-10">real</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-8-3"
4 years ago
class="td11"><!--l. 578--><p class="noindent" ><span
class="cmr-10">Any real number</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-8-4"
4 years ago
class="td11"><!--l. 579--><p class="noindent" ><span
class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-8-5"
4 years ago
class="td11"><!--l. 580--><p class="noindent" ><span
class="cmr-10">Set an entry in the MUMPS real control</span>
<span
class="cmr-10">array, as chosen via the </span><span class="lstinline"></span><span
class="cmtt-10">idx</span> <span
class="cmr-10">optional</span>
4 years ago
<span
class="cmr-10">argument.</span> </td>
4 years ago
</tr><tr
class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
style="vertical-align:baseline;" id="TBL-9-9-"><td style="white-space:wrap; text-align:left;" id="TBL-9-9-1"
class="td11"> </td></tr></table></div></div>
4 years ago
<br /> <div class="caption"
><span class="id">Table&#x00A0;7: </span><span
4 years ago
class="content">Parameters defining the smoother or the details of the one-level preconditioner
(continued).</span></div><!--tex4ht:label?: x17-16014r7 -->
4 years ago
</div><hr class="endfloat" />
</div>
4 years ago
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