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   <h4 class="subsectionHead"><span class="titlemark"><span 
class="cmr-12">5.2   </span></span> <a 
 id="x19-180005.2"></a><span 
class="cmr-12">Method set</span></h4>
<div class="center" 
>
<!--l. 74--><p class="noindent" >
<!--l. 75--><p class="noindent" ><span class="lstinline"></span><span 
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>
<!--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 
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 
class="cmr-12">.</span>
<!--l. 83--><p class="noindent" ><span 
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:normal; text-align:left;" id="TBL-3-1-1"  
class="td11"><!--l. 86--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">what</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-3-1-2"  
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 
class="cmr-12">.</span>                                                             </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-2-"><td  style="white-space:normal; text-align:left;" id="TBL-3-2-1"  
class="td11"><!--l. 87--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-2-2"  
class="td11"><!--l. 87--><p class="noindent" ><span 
class="cmr-12">The parameter to be set. It can be specified through its name; the</span>
<span 
class="cmr-12">string is case-insensitive. See Tables</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18009r2"><span 
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span 
class="cmr-12">-</span><a 
href="#x19-18015r8"><span 
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span 
class="cmr-12">.</span>                                  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-3-"><td  style="white-space:normal; text-align:left;" id="TBL-3-3-1"  
class="td11"><!--l. 90--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">val</span><span 
class="cmtt-12">&#x00A0;</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-3-3-2"  
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 
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 
class="cmr-12">.</span>                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-4-"><td  style="white-space:normal; text-align:left;" id="TBL-3-4-1"  
class="td11"><!--l. 93--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-4-2"  
class="td11"><!--l. 93--><p class="noindent" ><span 
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="#x19-18009r2"><span 
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span 
class="cmr-12">-</span><a 
href="#x19-18015r8"><span 
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span 
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 
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:normal; text-align:left;" id="TBL-3-5-1"  
class="td11"><!--l. 98--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">info</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-3-5-2"  
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 
class="cmr-12">.</span>                                                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-6-"><td  style="white-space:normal; text-align:left;" id="TBL-3-6-1"  
class="td11"><!--l. 99--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-6-2"  
class="td11"><!--l. 99--><p class="noindent" ><span 
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span 
class="cmr-12">&#x00A0;</span><a 
href="userhtmlse7.html#x28-320007"><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:normal; text-align:left;" id="TBL-3-7-1"  
class="td11"><!--l. 101--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">ilev</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-3-7-2"  
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 
class="cmr-12">.</span>                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-8-"><td  style="white-space:normal; text-align:left;" id="TBL-3-8-1"  
class="td11"><!--l. 102--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-8-2"  
class="td11"><!--l. 102--><p class="noindent" ><span 
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>
<span 
class="cmr-12">is set at all levels that are appropriate (see Tables</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18009r2"><span 
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span 
class="cmr-12">-</span><a 
href="#x19-18015r8"><span 
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span 
class="cmr-12">).</span>              </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-9-"><td  style="white-space:normal; text-align:left;" id="TBL-3-9-1"  
class="td11"><!--l. 109--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">ilmax</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-3-9-2"  
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 
class="cmr-12">.</span>                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-10-"><td  style="white-space:normal; text-align:left;" id="TBL-3-10-1"  
class="td11"><!--l. 110--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-10-2"  
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 
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 
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 
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:normal; text-align:left;" id="TBL-3-11-1"  
class="td11"><!--l. 117--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">pos</span>   </td><td  style="white-space:normal; text-align:left;" id="TBL-3-11-2"  
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>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-12-"><td  style="white-space:normal; text-align:left;" id="TBL-3-12-1"  
class="td11"><!--l. 118--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-12-2"  
class="td11"><!--l. 118--><p class="noindent" ><span 
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 
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 
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 
class="cmr-12">is ignored.</span>                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-13-"><td  style="white-space:normal; text-align:left;" id="TBL-3-13-1"  
class="td11"><!--l. 123--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-12">idx</span>   </td><td  style="white-space:normal; text-align:left;" id="TBL-3-13-2"  
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 
class="cmr-12">.</span>                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-3-14-"><td  style="white-space:normal; text-align:left;" id="TBL-3-14-1"  
class="td11"><!--l. 124--><p class="noindent" >      </td><td  style="white-space:normal; text-align:left;" id="TBL-3-14-2"  
class="td11"><!--l. 124--><p class="noindent" ><span 
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>
<!--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>
<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="x19-18002x1"><span 
class="cmr-12">the type of multilevel cycle and how many cycles must be applied;</span>
     </li>
     <li 
  class="enumerate" id="x19-18004x2"><span 
class="cmr-12">the coarsening algorithm;</span>
     </li>
     <li 
  class="enumerate" id="x19-18006x3"><span 
class="cmr-12">the solver at the coarsest level (for multilevel preconditioners only);</span>
     </li>
     <li 
  class="enumerate" id="x19-18008x4"><span 
class="cmr-12">the   smoother   of   the   multilevel   preconditioners,   or   the   one-level</span>
                                                                               

                                                                               
     <span 
class="cmr-12">preconditioner.</span></li></ol>
<!--l. 145--><p class="noindent" ><span 
class="cmr-12">A list of the parameters that can be set, along with their allowed and default values, is</span>
<span 
class="cmr-12">given in Tables</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18009r2"><span 
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span 
class="cmr-12">-</span><a 
href="#x19-18015r8"><span 
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span 
class="cmr-12">.</span><br 
class="newline" />
<!--l. 148--><p class="indent" >   <span 
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 
class="cmr-12">), as specified in</span>
<span 
class="cmr-12">Tables</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18014r7"><span 
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span 
class="cmr-12">-</span><a 
href="#x19-18015r8"><span 
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span 
class="cmr-12">. For example, the block-Jacobi smoother using ILU(0) on the blocks is</span>
<span 
class="cmr-12">obtained by combining the block-Jacobi smoother object with the ILU(0) solver</span>
<span 
class="cmr-12">object. Similarly, the hybrid Gauss-Seidel smoother (see Note in Table</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18014r7"><span 
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span 
class="cmr-12">) is</span>
<span 
class="cmr-12">obtained by combining the block-Jacobi smoother object with a single sweep of</span>
<span 
class="cmr-12">the Gauss-Seidel solver object, while the point-Jacobi smoother is the result</span>
<span 
class="cmr-12">of combining the block-Jacobi smoother object with a single sweep of the</span>
<span 
class="cmr-12">point-Jacobi solver object. In the same way are obtained the </span><span 
class="cmmi-12">&#x2113;</span><sub><span 
class="cmr-8">1</span></sub><span 
class="cmr-12">-versions of the</span>
<span 
class="cmr-12">smoothers. However, for simplicity, shortcuts are provided to set all versions of</span>
<span 
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 
class="cmr-12">to</span>
<span 
class="cmr-12">certain specific values (see Tables</span><span 
class="cmr-12">&#x00A0;</span><a 
href="#x19-18014r7"><span 
class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span 
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 
class="cmr-12">as</span>
<span 
class="cmr-12">well.</span>
<!--l. 166--><p class="indent" >   <span 
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 
class="cmr-12">smoother.</span>
<!--l. 175--><p class="indent" >   <span 
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><a 
href="#x19-18012r5"><span 
class="cmr-12">5</span><!--tex4ht:ref: tab:p_coarse_1 --></a><span 
class="cmr-12">).</span>
<br 
class="newline" />
<!--l. 179--><p class="indent" >   <span 
class="cmbx-12">Remark 3. </span><span 
class="cmr-12">Many of the coarsest-level solvers apply to a specific coarsest-matrix</span>
<span 
class="cmr-12">layout; therefore, setting the solver after the layout may change the layout to either</span>
<span 
class="cmr-12">distributed or replicated. Similarly, setting the layout after the solver may change the</span>
<span 
class="cmr-12">solver.</span>
<!--l. 185--><p class="indent" >   <span 
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 and KRM require it to be distributed. In these cases,</span>
<span 
class="cmr-12">setting the coarsest-level solver implies that the layout is redefined according to the</span>
<span 
class="cmr-12">solver, ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel</span>
<span 
class="cmr-12">and block-Jacobi can be applied to replicated and distributed matrices, thus their</span>
<span 
class="cmr-12">choice does not modify any previously specified layout. It is worth noting that, when</span>
<span 
class="cmr-12">the matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers</span>
<span 
class="cmr-12">and their </span><span 
class="cmmi-12">&#x2113;</span><sub><span 
class="cmr-8">1</span></sub><span 
class="cmsy-10x-x-120">- </span><span 
class="cmr-12">versions reduce to the corresponding local solver objects (see Remark</span><span 
class="cmr-12">&#x00A0;2).</span>
<span 
class="cmr-12">For the point-Jacobi and Gauss-Seidel solvers, these objects correspond to a </span><span 
class="cmti-12">single</span>
                                                                               

                                                                               
<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>
<!--l. 200--><p class="indent" >   <span 
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 chosen</span>
<span 
class="cmr-12">solver applied to the local blocks. Likewise, the replicated layout can be used with any</span>
<span 
class="cmr-12">solver but SuperLu</span><span 
class="cmr-12">_Dist and KRM; therefore, if SuperLu</span><span 
class="cmr-12">_Dist or KRM have 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>
<!--l. 208--><p class="indent" >   <span 
class="cmr-12">In a parallel setting with many cores, we suggest to the users to change the default</span>
<span 
class="cmr-12">coarsest solver for using the KRM choice, i.e. a parallel distributed iterative solution of</span>
<span 
class="cmr-12">the coarsest system based on Krylov methods.</span>
<!--l. 212--><p class="indent" >   <span 
class="cmbx-12">Remark 4. </span><span 
class="cmr-12">The argument </span><span class="lstinline"></span><span 
class="cmtt-12">idx</span> <span 
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 
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 
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#x27-310006"><span 
class="cmr-12">6</span><!--tex4ht:ref: sec:adding --></a><span 
class="cmr-12">.</span>
   <div class="table">
                                                                               

                                                                               
<!--l. 223--><p class="indent" >   <a 
 id="x19-18009r2"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 223--><p class="noindent" >
<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:normal; text-align:left;" id="TBL-4-1-1"  
class="td11"><!--l. 227--><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"  
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:normal; text-align:left;" id="TBL-4-1-3"  
class="td11"><!--l. 227--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>         </td><td  style="white-space:normal; text-align:left;" id="TBL-4-1-4"  
class="td11"><!--l. 227--><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:normal; text-align:left;" id="TBL-4-1-5"  
class="td11"><!--l. 228--><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-4-2-"><td  style="white-space:normal; text-align:left;" id="TBL-4-2-1"  
class="td11"><!--l. 229--><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"  
class="td11"><span class="lstinline"></span><!--l. 229--><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:normal; text-align:left;" id="TBL-4-2-3"  
class="td11"><!--l. 230--><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>
<!--l. 230--><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>
<!--l. 230--><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>
<!--l. 230--><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:normal; text-align:left;" id="TBL-4-2-4"  
class="td11"><!--l. 231--><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:normal; text-align:left;" id="TBL-4-2-5"  
class="td11"><!--l. 232--><p class="noindent" >Multilevel cycle: V-cycle, W-cycle, K-cycle,
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:normal; text-align:left;" id="TBL-4-3-1"  
class="td11"><!--l. 233--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">CYCLE_SWEEPS</span><span 
class="cmtt-10x-x-109">&#8217;</span>    </td><td  style="white-space:nowrap; text-align:left;" id="TBL-4-3-2"  
class="td11"><span class="lstinline"></span><!--l. 233--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-4-3-3"  
class="td11"><!--l. 234--><p class="noindent" >Any integer
<!--l. 234--><p class="noindent" >number <span 
class="cmsy-10x-x-109">&#x2265; </span>1   </td><td  style="white-space:normal; text-align:left;" id="TBL-4-3-4"  
class="td11"><!--l. 234--><p class="noindent" >1                 </td><td  style="white-space:normal; text-align:left;" id="TBL-4-3-5"  
class="td11"><!--l. 235--><p class="noindent" >Number of multilevel cycles.                   </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-4-4-"><td  style="white-space:normal; text-align:left;" id="TBL-4-4-1"  
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?: x19-18009r2 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 245--><p class="indent" >   <a 
 id="x19-18010r3"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 245--><p class="noindent" >
                                                                               

                                                                               
<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:normal; text-align:left;" id="TBL-5-1-1"  
class="td11"><!--l. 249--><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"  
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:normal; text-align:left;" id="TBL-5-1-3"  
class="td11"><!--l. 249--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>        </td><td  style="white-space:normal; text-align:left;" id="TBL-5-1-4"  
class="td11"><!--l. 249--><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:normal; text-align:left;" id="TBL-5-1-5"  
class="td11"><!--l. 250--><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-5-2-"><td  style="white-space:normal; text-align:left;" id="TBL-5-2-1"  
class="td11"><!--l. 251--><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"  
class="td11"><span class="lstinline"></span><!--l. 251--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>   </td><td  style="white-space:normal; text-align:left;" id="TBL-5-2-3"  
class="td11"><!--l. 252--><p class="noindent" >Any number
<!--l. 252--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003E; </span>0             </td><td  style="white-space:normal; text-align:left;" id="TBL-5-2-4"  
class="td11"><!--l. 253--><p class="noindent" >200               </td><td  style="white-space:normal; text-align:left;" id="TBL-5-2-5"  
class="td11"><!--l. 254--><p class="noindent" >Coarse  size  threshold  per  process.  The
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
(see Note).                                        </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-5-3-"><td  style="white-space:normal; text-align:left;" id="TBL-5-3-1"  
class="td11"><!--l. 260--><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"  
class="td11"><span class="lstinline"></span><!--l. 260--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-5-3-3"  
class="td11"><!--l. 261--><p class="noindent" >Any number
<!--l. 261--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003E; </span>0             </td><td  style="white-space:normal; text-align:left;" id="TBL-5-3-4"  
class="td11"><!--l. 262--><p class="noindent" >-1                 </td><td  style="white-space:normal; text-align:left;" id="TBL-5-3-5"  
class="td11"><!--l. 263--><p class="noindent" >Coarse  size  threshold.  The  aggregation
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>
</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:normal; text-align:left;" id="TBL-5-4-1"  
class="td11"><!--l. 272--><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"  
class="td11"><span class="lstinline"></span><!--l. 272--><p class="noindent" ><span 
class="cmtt-10x-x-109">real</span>                                                                     </td><td  style="white-space:normal; text-align:left;" id="TBL-5-4-3"  
class="td11"><!--l. 273--><p class="noindent" >Any number
<!--l. 273--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003E; </span>1             </td><td  style="white-space:normal; text-align:left;" id="TBL-5-4-4"  
class="td11"><!--l. 274--><p class="noindent" >1.5                </td><td  style="white-space:normal; text-align:left;" id="TBL-5-4-5"  
class="td11"><!--l. 275--><p class="noindent" >Minimum                           coarsening
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>
</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:normal; text-align:left;" id="TBL-5-5-1"  
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">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"  
class="td11"><span class="lstinline"></span><!--l. 280--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-5-5-3"  
class="td11"><!--l. 281--><p class="noindent" >Any integer
<!--l. 281--><p class="noindent" >number <span 
class="cmmi-10x-x-109">&#x003E; </span>1  </td><td  style="white-space:normal; text-align:left;" id="TBL-5-5-4"  
class="td11"><!--l. 282--><p class="noindent" >20                </td><td  style="white-space:normal; text-align:left;" id="TBL-5-5-5"  
class="td11"><!--l. 283--><p class="noindent" >Maximum    number    of    levels.    The
aggregation stops if the number of levels
reaches this value (see Note).               </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-5-6-"><td  style="white-space:normal; text-align:left;" id="TBL-5-6-1"  
class="td11"><!--l. 285--><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"  
class="td11"><span class="lstinline"></span><!--l. 285--><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:normal; text-align:left;" id="TBL-5-6-3"  
class="td11"><!--l. 286--><p class="noindent" ><span 
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:normal; text-align:left;" id="TBL-5-6-4"  
class="td11"><!--l. 287--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;DEC&#8217;</span>       </td><td  style="white-space:normal; text-align:left;" id="TBL-5-6-5"  
class="td11"><!--l. 288--><p class="noindent" >Parallel aggregation algorithm.
<!--l. 288--><p class="noindent" >the  <span class="lstinline"></span><span 
class="cmtt-10x-x-109">SYMDEC</span>  option  applies  decoupled
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>
</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:normal; text-align:left;" id="TBL-5-7-1"  
class="td11"><!--l. 305--><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-5-7-2"  
class="td11"><span class="lstinline"></span><!--l. 305--><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:normal; text-align:left;" id="TBL-5-7-3"  
class="td11"><!--l. 306--><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:normal; text-align:left;" id="TBL-5-7-4"  
class="td11"><!--l. 309--><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:normal; text-align:left;" id="TBL-5-7-5"  
class="td11"><!--l. 310--><p class="noindent" >Type of aggregation algorithm: currently,
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="userhtmlli5.html#XVANEK_MANDEL_BREZINA">33</a>]</span>,
and the one by Gratton et al&#x00A0;<span class="cite">[<a 
href="userhtmlli5.html#XGrHeJi:16">23</a>]</span>. The
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="userhtmlli5.html#XMatchBoxP">9</a>]</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:normal; text-align:left;" id="TBL-5-8-1"  
class="td11"><!--l. 318--><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-5-8-2"  
class="td11"><span class="lstinline"></span><!--l. 318--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-5-8-3"  
class="td11"><!--l. 319--><p class="noindent" >Any integer
<!--l. 319--><p class="noindent" >power   of   2,
with
<span 
class="cmtt-10x-x-109">aggr</span><span 
class="cmtt-10x-x-109">_size</span> <span 
class="cmsy-10x-x-109">&#x2265;</span>
2                </td><td  style="white-space:normal; text-align:left;" id="TBL-5-8-4"  
class="td11"><!--l. 320--><p class="noindent" >4                  </td><td  style="white-space:normal; text-align:left;" id="TBL-5-8-5"  
class="td11"><!--l. 321--><p class="noindent" >Maximum  size  of  aggregates  when  the
coupled  aggregation  based  on  matching
is   applied.   For   aggressive   coarsening
with  size  of  aggregate  larger  than  8
we  recommend  the  use  of  smoothed
prolongators. Used only with <span 
class="cmtt-10x-x-109">&#8217;COUPLED&#8217;</span>
and <span 
class="cmtt-10x-x-109">&#8217;MATCHBOXP&#8217;</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-5-9-"><td  style="white-space:normal; text-align:left;" id="TBL-5-9-1"  
class="td11"><!--l. 326--><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-5-9-2"  
class="td11"><span class="lstinline"></span><!--l. 326--><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:normal; text-align:left;" id="TBL-5-9-3"  
class="td11"><!--l. 327--><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:normal; text-align:left;" id="TBL-5-9-4"  
class="td11"><!--l. 327--><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:normal; text-align:left;" id="TBL-5-9-5"  
class="td11"><!--l. 328--><p class="noindent" >Prolongator  used  by  the  aggregation
algorithm: smoothed or unsmoothed (i.e.,
tentative prolongator).                        </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-5-10-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-5-10-1"  
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>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-5-11-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-5-11-1"  
class="td11"></td><div class="multicolumn"  style="white-space:nowrap; text-align:left;">the minimum coarsening ratio, or the maximum number of levels is reached.</div>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-5-12-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-5-12-1"  
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>
</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-5-13-"><td  style="white-space:normal; text-align:left;" id="TBL-5-13-1"  
class="td11">                             </td></tr></table>
                                                                               

                                                                               
</div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;3: </span><span  
class="content">Parameters defining the aggregation algorithm. </span></div><!--tex4ht:label?: x19-18010r3 -->
</div>
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 346--><p class="indent" >   <a 
 id="x19-18011r4"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 346--><p class="noindent" >
<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:normal; text-align:left;" id="TBL-6-1-1"  
class="td11"><!--l. 350--><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"  
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:normal; text-align:left;" id="TBL-6-1-3"  
class="td11"><!--l. 350--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>         </td><td  style="white-space:normal; text-align:left;" id="TBL-6-1-4"  
class="td11"><!--l. 350--><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:normal; text-align:left;" id="TBL-6-1-5"  
class="td11"><!--l. 351--><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-6-2-"><td  style="white-space:normal; text-align:left;" id="TBL-6-2-1"  
class="td11"><!--l. 353--><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"  
class="td11"><span class="lstinline"></span><!--l. 353--><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:normal; text-align:left;" id="TBL-6-2-3"  
class="td11"><!--l. 354--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;NATURAL&#8217;</span>
<!--l. 354--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;DEGREE&#8217;</span>    </td><td  style="white-space:normal; text-align:left;" id="TBL-6-2-4"  
class="td11"><!--l. 355--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;NATURAL&#8217;</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-6-2-5"  
class="td11"><!--l. 356--><p class="noindent" >Initial    ordering    of    indices    for
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:normal; text-align:left;" id="TBL-6-3-1"  
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_THRESH</span><span 
class="cmtt-10x-x-109">&#8217;</span>      </td><td  style="white-space:nowrap; text-align:left;" id="TBL-6-3-2"  
class="td11"><span class="lstinline"></span><!--l. 363--><p class="noindent" ><span 
class="cmtt-10x-x-109">real</span><span 
class="cmtt-10x-x-109">(</span><span 
class="cmtt-10x-x-109">kind_parameter</span><span 
class="cmtt-10x-x-109">)</span>                                                     </td><td  style="white-space:normal; text-align:left;" id="TBL-6-3-3"  
class="td11"><!--l. 364--><p class="noindent" >Any&#x00A0;real
<!--l. 364--><p class="noindent" >number&#x00A0;<span 
class="cmsy-10x-x-109">&#x2208;</span>
[0<span 
class="cmmi-10x-x-109">,</span>1]             </td><td  style="white-space:normal; text-align:left;" id="TBL-6-3-4"  
class="td11"><!--l. 365--><p class="noindent" >0.01             </td><td  style="white-space:normal; text-align:left;" id="TBL-6-3-5"  
class="td11"><!--l. 366--><p class="noindent" >The  threshold  <span 
class="cmmi-10x-x-109">&#x03B8;  </span>in  the  strength  of
connection algorithm. 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:normal; text-align:left;" id="TBL-6-4-1"  
class="td11"><!--l. 369--><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"  
class="td11"><span class="lstinline"></span><!--l. 370--><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:normal; text-align:left;" id="TBL-6-4-3"  
class="td11"><!--l. 371--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;FILTER&#8217;</span>
<!--l. 371--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;NOFILTER&#8217;</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-6-4-4"  
class="td11"><!--l. 372--><p class="noindent" ><span 
class="cmtt-10x-x-109">&#8217;NOFILTER&#8217;</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-6-4-5"  
class="td11"><!--l. 373--><p class="noindent" >Matrix used in computing the smoothed
prolongator: filtered or unfiltered.       </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:normal; text-align:left;" id="TBL-6-5-1"  
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="userhtmlli5.html#XVANEK_MANDEL_BREZINA">33</a>, Section&#x00A0;5.1]</span>, can be easily set by invoking the rou-</div>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-6-6-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-6-6-1"  
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:normal; text-align:left;" id="TBL-6-7-1"  
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?: x19-18011r4 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 390--><p class="indent" >   <a 
 id="x19-18012r5"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 390--><p class="noindent" >
                                                                               

                                                                               
<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:normal; text-align:left;" id="TBL-7-1-1"  
class="td11"><!--l. 393--><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"  
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:normal; text-align:left;" id="TBL-7-1-3"  
class="td11"><!--l. 393--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>      </td><td  style="white-space:normal; text-align:left;" id="TBL-7-1-4"  
class="td11"><!--l. 393--><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:normal; text-align:left;" id="TBL-7-1-5"  
class="td11"><!--l. 394--><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-7-2-"><td  style="white-space:normal; text-align:left;" id="TBL-7-2-1"  
class="td11"><!--l. 395--><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"  
class="td11"><span class="lstinline"></span><!--l. 395--><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:normal; text-align:left;" id="TBL-7-2-3"  
class="td11"><!--l. 396--><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>
<!--l. 396--><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:normal; text-align:left;" id="TBL-7-2-4"  
class="td11"><!--l. 397--><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:normal; text-align:left;" id="TBL-7-2-5"  
class="td11"><!--l. 398--><p class="noindent" >Coarsest  matrix  layout:  distributed  among  the
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:normal; text-align:left;" id="TBL-7-3-1"  
class="td11"><!--l. 400--><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"  
class="td11"><span class="lstinline"></span><!--l. 400--><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:normal; text-align:left;" id="TBL-7-3-3"  
class="td11"><!--l. 401--><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>
<!--l. 401--><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>
<!--l. 402--><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>
<!--l. 402--><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>
<!--l. 403--><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>
<!--l. 404--><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>
<!--l. 405--><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>
<!--l. 406--><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>
<!--l. 407--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 408--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">L1</span><span 
class="cmtt-10x-x-109">-</span><span 
class="cmtt-10x-x-109">JACOBI</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 409--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">L1</span><span 
class="cmtt-10x-x-109">-</span><span 
class="cmtt-10x-x-109">BJAC</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 410--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">L1</span><span 
class="cmtt-10x-x-109">-</span><span 
class="cmtt-10x-x-109">FBGS</span><span 
class="cmtt-10x-x-109">&#8217;</span></td><td  style="white-space:normal; text-align:left;" id="TBL-7-3-4"  
class="td11"><!--l. 411--><p class="noindent" >See&#x00A0;Note.</td><td  style="white-space:normal; text-align:left;" id="TBL-7-3-5"  
class="td11"><!--l. 412--><p class="noindent" >Solver   used   at   the   coarsest   level:   sequential
LU   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 
class="cmmi-10x-x-109">&#x2113;</span><sub><span 
class="cmr-8">1</span></sub>-versions;  Krylov  Method  (flexible
Conjugate Gradient) coupled with the block-Jacobi
preconditioner  with  ILU(0)  on  the  blocks.  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 
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">KRM</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
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:normal; text-align:left;" id="TBL-7-4-1"  
class="td11"><!--l. 442--><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"  
class="td11"><span class="lstinline"></span><!--l. 442--><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:normal; text-align:left;" id="TBL-7-4-3"  
class="td11"><!--l. 443--><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>
<!--l. 443--><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>
<!--l. 443--><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>
<!--l. 444--><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>
<!--l. 444--><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>
<!--l. 444--><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>
<!--l. 445--><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>
<!--l. 445--><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>
<!--l. 445--><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:normal; text-align:left;" id="TBL-7-4-4"  
class="td11"><!--l. 446--><p class="noindent" >See&#x00A0;Note.</td><td  style="white-space:normal; text-align:left;" id="TBL-7-4-5"  
class="td11"><!--l. 447--><p class="noindent" >Solver  for  the  diagonal  blocks  of  the  coarsest
matrix, 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),   Approximate   Inverses
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>); note
that  approximate  inverses  are  specifically  suited
for  GPUs  since  they  do  not  employ  triangular
system solve kernels, see&#x00A0;<span class="cite">[<a 
href="userhtmlli5.html#XBERTACCINIFILIPPONE">3</a>]</span>. Note that 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-7-5-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-5-1"  
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:normal; text-align:left;" id="TBL-7-6-1"  
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:normal; text-align:left;" id="TBL-7-7-1"  
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:normal; text-align:left;" id="TBL-7-8-1"  
class="td11"><!--l. 478--><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"  
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:normal; text-align:left;" id="TBL-7-8-3"  
class="td11"><!--l. 478--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>      </td><td  style="white-space:normal; text-align:left;" id="TBL-7-8-4"  
class="td11"><!--l. 478--><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:normal; text-align:left;" id="TBL-7-8-5"  
class="td11"><!--l. 479--><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-7-9-"><td  style="white-space:normal; text-align:left;" id="TBL-7-9-1"  
class="td11"><!--l. 480--><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"  
class="td11"><span class="lstinline"></span><!--l. 480--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-7-9-3"  
class="td11"><!--l. 481--><p class="noindent" >Any
integer
<!--l. 481--><p class="noindent" >number   <span 
class="cmmi-10x-x-109">&#x003E;</span>
0             </td><td  style="white-space:normal; text-align:left;" id="TBL-7-9-4"  
class="td11"><!--l. 482--><p class="noindent" >10          </td><td  style="white-space:normal; text-align:left;" id="TBL-7-9-5"  
class="td11"><!--l. 483--><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.                           </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-7-10-"><td  style="white-space:normal; text-align:left;" id="TBL-7-10-1"  
class="td11"><!--l. 485--><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"  
class="td11"><span class="lstinline"></span><!--l. 485--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-7-10-3"  
class="td11"><!--l. 486--><p class="noindent" >Any
integer
<!--l. 486--><p class="noindent" >number   <span 
class="cmsy-10x-x-109">&#x2265;</span>
0             </td><td  style="white-space:normal; text-align:left;" id="TBL-7-10-4"  
class="td11"><!--l. 487--><p class="noindent" >0            </td><td  style="white-space:normal; text-align:left;" id="TBL-7-10-5"  
class="td11"><!--l. 488--><p class="noindent" >Fill-in  level  <span 
class="cmmi-10x-x-109">p </span>of  the  ILU  factorizations  and  first
fill-in for the approximate inverses.                     </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-7-11-"><td  style="white-space:normal; text-align:left;" id="TBL-7-11-1"  
class="td11"><!--l. 490--><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"  
class="td11"><span class="lstinline"></span><!--l. 491--><p class="noindent" ><span 
class="cmtt-10x-x-109">real</span><span 
class="cmtt-10x-x-109">(</span><span 
class="cmtt-10x-x-109">kind_parameter</span><span 
class="cmtt-10x-x-109">)</span>                                                     </td><td  style="white-space:normal; text-align:left;" id="TBL-7-11-3"  
class="td11"><!--l. 492--><p class="noindent" >Any real
<!--l. 492--><p class="noindent" >number   <span 
class="cmsy-10x-x-109">&#x2265;</span>
0             </td><td  style="white-space:normal; text-align:left;" id="TBL-7-11-4"  
class="td11"><!--l. 493--><p class="noindent" >0            </td><td  style="white-space:normal; text-align:left;" id="TBL-7-11-5"  
class="td11"><!--l. 494--><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 and
first drop-tolerance for the approximate inverses.   </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-7-12-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-12-1"  
class="td11"></td><div class="multicolumn"  style="white-space:nowrap; text-align:left;"><span 
class="cmbx-10x-x-109">Note. </span>Further options for coarse solvers are contained in Table&#x00A0;<a 
href="#x19-18013r6">6<!--tex4ht:ref: tab:p_coarse_2 --></a>.</div>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-7-13-"><td colspan="3" style="white-space:normal; text-align:left;" id="TBL-7-13-1"  
class="td11"></td><div class="multicolumn"  style="white-space:nowrap; text-align:left;">For a first use it is suggested to use the default options obtained by simply selecting the solver type.</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-7-14-"><td  style="white-space:normal; text-align:left;" id="TBL-7-14-1"  
class="td11">                    </td></tr></table>
                                                                               

                                                                               
</div></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;5: </span><span  
class="content">Parameters defining the solver at the coarsest level (continued).</span></div><!--tex4ht:label?: x19-18012r5 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 507--><p class="indent" >   <a 
 id="x19-18013r6"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 507--><p class="noindent" >
                                                                               

                                                                               
<div class="tabular"> <table id="TBL-8" class="tabular" 
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 
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:normal; text-align:left;" id="TBL-8-1-1"  
class="td11"><!--l. 510--><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-8-1-2"  
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:normal; text-align:left;" id="TBL-8-1-3"  
class="td11"><!--l. 510--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">val</span>       </td><td  style="white-space:normal; text-align:left;" id="TBL-8-1-4"  
class="td11"><!--l. 510--><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:normal; text-align:left;" id="TBL-8-1-5"  
class="td11"><!--l. 511--><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-8-2-"><td  style="white-space:normal; text-align:left;" id="TBL-8-2-1"  
class="td11"><!--l. 512--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BJAC_STOP</span><span 
class="cmtt-10x-x-109">&#8217;</span> </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-2-2"  
class="td11"><span class="lstinline"></span><!--l. 512--><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:normal; text-align:left;" id="TBL-8-2-3"  
class="td11"><!--l. 512--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 512--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">TRUE</span><span 
class="cmtt-10x-x-109">&#8217;</span>    </td><td  style="white-space:normal; text-align:left;" id="TBL-8-2-4"  
class="td11"><!--l. 512--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-2-5"  
class="td11"><!--l. 512--><p class="noindent" >Select whether to use a stopping criterion for
the  Block-Jacobi  method  used  as  a  coarse
solver.                                                    </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:normal; text-align:left;" id="TBL-8-3-1"  
class="td11"><!--l. 513--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BJAC_TRACE</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-3-2"  
class="td11"><span class="lstinline"></span><!--l. 513--><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:normal; text-align:left;" id="TBL-8-3-3"  
class="td11"><!--l. 513--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 513--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">TRUE</span><span 
class="cmtt-10x-x-109">&#8217;</span>    </td><td  style="white-space:normal; text-align:left;" id="TBL-8-3-4"  
class="td11"><!--l. 513--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-3-5"  
class="td11"><!--l. 513--><p class="noindent" >Select  whether  to  print  a  trace  for  the
calculated   residual   for   the   Block-Jacobi
method used as a coarse solver.                   </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:normal; text-align:left;" id="TBL-8-4-1"  
class="td11"><!--l. 514--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BJAC_ITRACE</span><span 
class="cmtt-10x-x-109">&#8217;</span>       </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-4-2"  
class="td11"><span class="lstinline"></span><!--l. 514--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-4-3"  
class="td11"><!--l. 514--><p class="noindent" >Any integer
<!--l. 514--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003E; </span>0           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-4-4"  
class="td11"><!--l. 514--><p class="noindent" >-1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-4-5"  
class="td11"><!--l. 514--><p class="noindent" >Number of iterations after which a trace is to
be printed.                                              </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:normal; text-align:left;" id="TBL-8-5-1"  
class="td11"><!--l. 515--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BJAC_RESCHECK</span><span 
class="cmtt-10x-x-109">&#8217;</span>     </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-5-2"  
class="td11"><span class="lstinline"></span><!--l. 515--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-5-3"  
class="td11"><!--l. 515--><p class="noindent" >Any integer
<!--l. 515--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003E; </span>0           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-5-4"  
class="td11"><!--l. 515--><p class="noindent" >-1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-5-5"  
class="td11"><!--l. 515--><p class="noindent" >Number of iterations after which a residual is
to be calculated.                                      </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:normal; text-align:left;" id="TBL-8-6-1"  
class="td11"><!--l. 516--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BJAC_STOPTOL</span><span 
class="cmtt-10x-x-109">&#8217;</span>      </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-6-2"  
class="td11"><span class="lstinline"></span><!--l. 516--><p class="noindent" ><span 
class="cmtt-10x-x-109">real</span><span 
class="cmtt-10x-x-109">(</span><span 
class="cmtt-10x-x-109">kind_parameter</span><span 
class="cmtt-10x-x-109">)</span>                                                     </td><td  style="white-space:normal; text-align:left;" id="TBL-8-6-3"  
class="td11"><!--l. 516--><p class="noindent" >Any real
<!--l. 516--><p class="noindent" ><span 
class="cmmi-10x-x-109">&#x003C; </span>1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-6-4"  
class="td11"><!--l. 516--><p class="noindent" >0            </td><td  style="white-space:normal; text-align:left;" id="TBL-8-6-5"  
class="td11"><!--l. 516--><p class="noindent" >Tolerance  for  the  stopping  criterion  on  the
residual.                                                 </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-8-7-"><td  style="white-space:normal; text-align:left;" id="TBL-8-7-1"  
class="td11"><!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_METHOD</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-7-2"  
class="td11"><span class="lstinline"></span><!--l. 517--><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:normal; text-align:left;" id="TBL-8-7-3"  
class="td11"><!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">CG</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FCG</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">CGS</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">CGR</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BICG</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BICGSTAB</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">BICGSTABL</span><span 
class="cmtt-10x-x-109">&#8217;</span>
<!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">RGMRES</span><span 
class="cmtt-10x-x-109">&#8217;</span>  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-7-4"  
class="td11"><!--l. 517--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FCG</span><span 
class="cmtt-10x-x-109">&#8217;</span>   </td><td  style="white-space:normal; text-align:left;" id="TBL-8-7-5"  
class="td11"><!--l. 517--><p class="noindent" >A string that defines the iterative method to
be  used  when  employing  a  Krylov  method
<span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM</span><span 
class="cmtt-10x-x-109">&#8217;</span> as  a  coarse  solver.  <span 
class="cmtt-10x-x-109">CG </span>the  Conjugate
Gradient method; <span 
class="cmtt-10x-x-109">FCG </span>the Flexible Conjugate
Gradient method; <span 
class="cmtt-10x-x-109">CGS </span>the Conjugate Gradient
Stabilized
method;   <span 
class="cmtt-10x-x-109">GCR  </span>the   Generalized   Conjugate
Residual method; <span 
class="cmtt-10x-x-109">FCG </span>the Flexible Conjugate
Gradient  method;  <span 
class="cmtt-10x-x-109">BICG  </span>the  Bi-Conjugate
Gradient method; <span 
class="cmtt-10x-x-109">BICGSTAB </span>the Bi-Conjugate
Gradient  Stabilized  method;  <span 
class="cmtt-10x-x-109">BICGSTABL </span>the
Bi-Conjugate   Gradient   Stabilized   method
with   restarting;   <span 
class="cmtt-10x-x-109">RGMRES  </span>the   Generalized
Minimal  Residual  method  with  restarting.
Refer to the PSBLAS guide&#x00A0;<span class="cite">[<a 
href="userhtmlli5.html#XPSBLASGUIDE">20</a>]</span> for further
information.                                            </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-8-8-"><td  style="white-space:normal; text-align:left;" id="TBL-8-8-1"  
class="td11"><!--l. 527--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_KPREC</span><span 
class="cmtt-10x-x-109">&#8217;</span>         </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-8-2"  
class="td11"><span class="lstinline"></span><!--l. 527--><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:normal; text-align:left;" id="TBL-8-8-3"  
class="td11"><!--l. 527--><p class="noindent" >Table&#x00A0;<a 
href="userhtmlse4.html#x14-13015r1">1<!--tex4ht:ref: tab:precinit --></a> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-8-4"  
class="td11"><!--l. 527--><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> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-8-5"  
class="td11"><!--l. 527--><p class="noindent" >The     one-level
preconditioners from the Table&#x00A0;<a 
href="userhtmlse4.html#x14-13015r1">1<!--tex4ht:ref: tab:precinit --></a> can be used
for the coarse Krylov solver.                       </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-8-9-"><td  style="white-space:normal; text-align:left;" id="TBL-8-9-1"  
class="td11"><!--l. 539--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_SUB_SOLVE</span><span 
class="cmtt-10x-x-109">&#8217;</span>     </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-9-2"  
class="td11"><span class="lstinline"></span><!--l. 539--><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:normal; text-align:left;" id="TBL-8-9-3"  
class="td11"><!--l. 539--><p class="noindent" >Table&#x00A0;<a 
href="#x19-18012r5">5<!--tex4ht:ref: tab:p_coarse_1 --></a> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-9-4"  
class="td11"><!--l. 539--><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> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-9-5"  
class="td11"><!--l. 539--><p class="noindent" >Solver for the diagonal blocks of the coarsest
matrix preconditioner, in case the block Jacobi
solver                     is                     chosen
as <span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_KPREC</span><span 
class="cmtt-10x-x-109">&#8217;</span>: 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), Approximate Inverses
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>);
The same caveat from Table&#x00A0;<a 
href="#x19-18012r5">5<!--tex4ht:ref: tab:p_coarse_1 --></a> applies here.  </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-8-10-"><td  style="white-space:normal; text-align:left;" id="TBL-8-10-1"  
class="td11"><!--l. 546--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_GLOBAL</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-10-2"  
class="td11"><span class="lstinline"></span><!--l. 546--><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:normal; text-align:left;" id="TBL-8-10-3"  
class="td11"><!--l. 546--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">TRUE</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">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span>   </td><td  style="white-space:normal; text-align:left;" id="TBL-8-10-4"  
class="td11"><!--l. 546--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">FALSE</span><span 
class="cmtt-10x-x-109">&#8217;</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-10-5"  
class="td11"><!--l. 546--><p class="noindent" >Choose  between  a  global  Krylov  solver,  all
unknowns on a single node, or a distributed
one.  The  default  choice  is  the  distributed
solver.                                                    </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-8-11-"><td  style="white-space:normal; text-align:left;" id="TBL-8-11-1"  
class="td11"><!--l. 547--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_EPS</span><span 
class="cmtt-10x-x-109">&#8217;</span>           </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-11-2"  
class="td11"><span class="lstinline"></span><!--l. 547--><p class="noindent" ><span 
class="cmtt-10x-x-109">real</span><span 
class="cmtt-10x-x-109">(</span><span 
class="cmtt-10x-x-109">kind_parameter</span><span 
class="cmtt-10x-x-109">)</span>                                                     </td><td  style="white-space:normal; text-align:left;" id="TBL-8-11-3"  
class="td11"><!--l. 547--><p class="noindent" >Real <span 
class="cmmi-10x-x-109">&#x003C; </span>1 </td><td  style="white-space:normal; text-align:left;" id="TBL-8-11-4"  
class="td11"><!--l. 547--><p class="noindent" >10<sup><span 
class="cmsy-8">-</span><span 
class="cmr-8">6</span> </sup> </td><td  style="white-space:normal; text-align:left;" id="TBL-8-11-5"  
class="td11"><!--l. 547--><p class="noindent" >The stopping tolerance.                </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-8-12-"><td  style="white-space:normal; text-align:left;" id="TBL-8-12-1"  
class="td11"><!--l. 548--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_IRST</span><span 
class="cmtt-10x-x-109">&#8217;</span>          </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-12-2"  
class="td11"><span class="lstinline"></span><!--l. 548--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-12-3"  
class="td11"><!--l. 548--><p class="noindent" >Integer
<!--l. 548--><p class="noindent" ><span 
class="cmsy-10x-x-109">&#x2265; </span>1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-12-4"  
class="td11"><!--l. 548--><p class="noindent" >30          </td><td  style="white-space:normal; text-align:left;" id="TBL-8-12-5"  
class="td11"><!--l. 548--><p class="noindent" >An integer specifying the restart parameter.
This is employed for the <span 
class="cmtt-10x-x-109">BiCGSTABL </span>or <span 
class="cmtt-10x-x-109">RGMRES</span>
methods, otherwise it is ignored.                 </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-8-13-"><td  style="white-space:normal; text-align:left;" id="TBL-8-13-1"  
class="td11"><!--l. 549--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_ISTOPC</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-13-2"  
class="td11"><span class="lstinline"></span><!--l. 549--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-13-3"  
class="td11"><!--l. 549--><p class="noindent" >Integers
1,2,3         </td><td  style="white-space:normal; text-align:left;" id="TBL-8-13-4"  
class="td11"><!--l. 549--><p class="noindent" >2            </td><td  style="white-space:normal; text-align:left;" id="TBL-8-13-5"  
class="td11"><!--l. 549--><p class="noindent" >If  <span 
class="cmtt-10x-x-109">1 </span>then  the  method  uses  the  normwise
backward error in the infinity norm; if <span 
class="cmtt-10x-x-109">2</span>, the
it uses the relative residual in the 2-norm; if <span 
class="cmtt-10x-x-109">3</span>
the relative residual reduction in the 2-norm is
used instead; refer to the PSBLAS&#x00A0;<span class="cite">[<a 
href="userhtmlli5.html#XPSBLASGUIDE">20</a>]</span> guide
for the details.                                         </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-8-14-"><td  style="white-space:normal; text-align:left;" id="TBL-8-14-1"  
class="td11"><!--l. 551--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_ITMAX</span><span 
class="cmtt-10x-x-109">&#8217;</span>         </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-14-2"  
class="td11"><span class="lstinline"></span><!--l. 551--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-14-3"  
class="td11"><!--l. 551--><p class="noindent" >Integer
<!--l. 551--><p class="noindent" ><span 
class="cmsy-10x-x-109">&#x2265; </span>1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-14-4"  
class="td11"><!--l. 551--><p class="noindent" >40          </td><td  style="white-space:normal; text-align:left;" id="TBL-8-14-5"  
class="td11"><!--l. 551--><p class="noindent" >The   maximum   number   of   iterations   to
perform.                                                 </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-8-15-"><td  style="white-space:normal; text-align:left;" id="TBL-8-15-1"  
class="td11"><!--l. 552--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_ITRACE</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-15-2"  
class="td11"><span class="lstinline"></span><!--l. 552--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-15-3"  
class="td11"><!--l. 552--><p class="noindent" >Integer
<!--l. 552--><p class="noindent" ><span 
class="cmsy-10x-x-109">&#x2265; </span>0           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-15-4"  
class="td11"><!--l. 552--><p class="noindent" >-1           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-15-5"  
class="td11"><!--l. 552--><p class="noindent" >If         <span 
class="cmmi-10x-x-109">&#x003E;             </span>0         print         out
an informational message about convergence
every <span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_ITRACE</span><span 
class="cmtt-10x-x-109">&#8217;</span> iterations. If = 0 print a
message in case of convergence failure.          </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-8-16-"><td  style="white-space:normal; text-align:left;" id="TBL-8-16-1"  
class="td11"><!--l. 556--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10x-x-109">&#8217;</span><span 
class="cmtt-10x-x-109">KRM_FILLIN</span><span 
class="cmtt-10x-x-109">&#8217;</span>        </td><td  style="white-space:nowrap; text-align:left;" id="TBL-8-16-2"  
class="td11"><span class="lstinline"></span><!--l. 556--><p class="noindent" ><span 
class="cmtt-10x-x-109">integer</span>                                                                  </td><td  style="white-space:normal; text-align:left;" id="TBL-8-16-3"  
class="td11"><!--l. 556--><p class="noindent" >Integer
<!--l. 556--><p class="noindent" ><span 
class="cmsy-10x-x-109">&#x2265; </span>0           </td><td  style="white-space:normal; text-align:left;" id="TBL-8-16-4"  
class="td11"><!--l. 557--><p class="noindent" >0            </td><td  style="white-space:normal; text-align:left;" id="TBL-8-16-5"  
class="td11"><!--l. 558--><p class="noindent" >Fill-in level <span 
class="cmmi-10x-x-109">p </span>of the ILU factorizations and
first fill-in for the approximate inverses.        </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-8-17-"><td  style="white-space:normal; text-align:left;" id="TBL-8-17-1"  
class="td11">                    </td></tr></table>                                                       

                                                                               
</div></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;6: </span><span  
class="content">Additional parameters defining the solver at the coarsest level.</span></div><!--tex4ht:label?: x19-18013r6 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 567--><p class="indent" >   <a 
 id="x19-18014r7"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 567--><p class="noindent" >
<div class="tabular"> <table id="TBL-9" class="tabular" 
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 
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:normal; text-align:left;" id="TBL-9-1-1"  
class="td11"><!--l. 571--><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"  
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:normal; text-align:left;" id="TBL-9-1-3"  
class="td11"><!--l. 571--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">val</span>       </td><td  style="white-space:normal; text-align:left;" id="TBL-9-1-4"  
class="td11"><!--l. 571--><p class="noindent" ><span 
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:normal; text-align:left;" id="TBL-9-1-5"  
class="td11"><!--l. 572--><p class="noindent" ><span 
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-9-2-"><td  style="white-space:normal; text-align:left;" id="TBL-9-2-1"  
class="td11"><!--l. 574--><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-9-2-2"  
class="td11"><span class="lstinline"></span><!--l. 574--><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:normal; text-align:left;" id="TBL-9-2-3"  
class="td11"><!--l. 575--><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>
<!--l. 575--><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>
<!--l. 575--><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>
<!--l. 575--><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>
<!--l. 576--><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>
<!--l. 576--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">L1</span><span 
class="cmtt-10">-</span><span 
class="cmtt-10">JACOBI</span><span 
class="cmtt-10">&#8217;</span>
<!--l. 576--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">L1</span><span 
class="cmtt-10">-</span><span 
class="cmtt-10">BJAC</span><span 
class="cmtt-10">&#8217;</span>
<!--l. 576--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">L1</span><span 
class="cmtt-10">-</span><span 
class="cmtt-10">FBGS</span><span 
class="cmtt-10">&#8217;</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-9-2-4"  
class="td11"><!--l. 577--><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:normal; text-align:left;" id="TBL-9-2-5"  
class="td11"><!--l. 578--><p class="noindent" ><span 
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="cmr-10">-Jacobi,</span>
<span 
class="cmmi-10">&#x2113;</span><sub><span 
class="cmr-7">1</span></sub><span 
class="cmr-10">&#8211;hybrid       (forward)       Gauss-Seidel,</span>
<span 
class="cmmi-10">&#x2113;</span><sub><span 
class="cmr-7">1</span></sub><span 
class="cmr-10">-point-Jacobi and Additive Schwarz.</span>
<!--l. 582--><p class="noindent" ><span 
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-9-3-"><td  style="white-space:normal; text-align:left;" id="TBL-9-3-1"  
class="td11"><!--l. 583--><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-9-3-2"  
class="td11"><span class="lstinline"></span><!--l. 583--><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:normal; text-align:left;" id="TBL-9-3-3"  
class="td11"><!--l. 584--><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>
<span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">GS</span><span 
class="cmtt-10">&#8217;</span>
<!--l. 585--><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>
<!--l. 585--><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>
<!--l. 586--><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>
<!--l. 586--><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>
<!--l. 587--><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>
<!--l. 588--><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>
<!--l. 588--><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>
<!--l. 589--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">INVT</span><span 
class="cmtt-10">&#8217;</span>
<!--l. 589--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">INVK</span><span 
class="cmtt-10">&#8217;</span>
<!--l. 589--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">&#8217;</span><span 
class="cmtt-10">AINV</span><span 
class="cmtt-10">&#8217;</span>    </td><td  style="white-space:normal; text-align:left;" id="TBL-9-3-4"  
class="td11"><!--l. 590--><p class="noindent" ><span 
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>
<!--l. 592--><p class="noindent" ><span 
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>           </td><td  style="white-space:normal; text-align:left;" id="TBL-9-3-5"  
class="td11"><!--l. 594--><p class="noindent" ><span 
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,</span>
<span 
class="cmr-10">SuperLU  or  UMFPACK  (plus  triangular</span>
<span 
class="cmr-10">solve), Approximate Inverses INVK(</span><span 
class="cmmi-10">p,q</span><span 
class="cmr-10">),</span>
<span 
class="cmr-10">INVT(</span><span 
class="cmmi-10">p</span><sub><span 
class="cmr-7">1</span></sub><span 
class="cmmi-10">,p</span><span 
class="cmr-10">2</span><span 
class="cmmi-10">,t</span><sub><span 
class="cmr-7">1</span></sub><span 
class="cmmi-10">,t</span><sub><span 
class="cmr-7">2</span></sub><span 
class="cmr-10">)   and   AINV(</span><span 
class="cmmi-10">t</span><span 
class="cmr-10">);   note</span>
<span 
class="cmr-10">that approximate inverses are specifically</span>
<span 
class="cmr-10">suited for GPUs since they do not employ</span>
<span 
class="cmr-10">triangular system solve kernels, see</span><span 
class="cmr-10">&#x00A0;</span><span class="cite"><span 
class="cmr-10">[</span><a 
href="userhtmlli5.html#XBERTACCINIFILIPPONE"><span 
class="cmr-10">3</span></a><span 
class="cmr-10">]</span></span><span 
class="cmr-10">. 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-9-4-"><td  style="white-space:normal; text-align:left;" id="TBL-9-4-1"  
class="td11"><!--l. 608--><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-9-4-2"  
class="td11"><span class="lstinline"></span><!--l. 608--><p class="noindent" ><span 
class="cmtt-10">integer</span>                                                                         </td><td  style="white-space:normal; text-align:left;" id="TBL-9-4-3"  
class="td11"><!--l. 609--><p class="noindent" ><span 
class="cmr-10">Any integer</span>
<!--l. 609--><p class="noindent" ><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:normal; text-align:left;" id="TBL-9-4-4"  
class="td11"><!--l. 610--><p class="noindent" ><span 
class="cmr-10">1</span>                             </td><td  style="white-space:normal; text-align:left;" id="TBL-9-4-5"  
class="td11"><!--l. 611--><p class="noindent" ><span 
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 
class="cmtt-10">&#8217;</span><span 
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-9-5-"><td  style="white-space:normal; text-align:left;" id="TBL-9-5-1"  
class="td11"><!--l. 616--><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-9-5-2"  
class="td11"><span class="lstinline"></span><!--l. 616--><p class="noindent" ><span 
class="cmtt-10">integer</span>                                                                         </td><td  style="white-space:normal; text-align:left;" id="TBL-9-5-3"  
class="td11"><!--l. 617--><p class="noindent" ><span 
class="cmr-10">Any integer</span>
<!--l. 617--><p class="noindent" ><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:normal; text-align:left;" id="TBL-9-5-4"  
class="td11"><!--l. 618--><p class="noindent" ><span 
class="cmr-10">1</span>                             </td><td  style="white-space:normal; text-align:left;" id="TBL-9-5-5"  
class="td11"><!--l. 619--><p class="noindent" ><span 
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-9-6-"><td  style="white-space:normal; text-align:left;" id="TBL-9-6-1"  
class="td11">                    </td></tr></table></div></div>
<br />  <div class="caption" 
><span class="id">Table&#x00A0;7:   </span><span  
class="content">Parameters   defining   the   smoother   or   the   details   of   the   one-level
preconditioner. </span></div><!--tex4ht:label?: x19-18014r7 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
   <div class="table">
                                                                               

                                                                               
<!--l. 628--><p class="indent" >   <a 
 id="x19-18015r8"></a><hr class="float"><div class="float" 
>
                                                                               

                                                                               
<div class="center" 
>
<!--l. 628--><p class="noindent" >
<div class="tabular"> <table id="TBL-10" class="tabular" 
cellspacing="0" cellpadding="0"  
><colgroup id="TBL-10-1g"><col 
id="TBL-10-1"></colgroup><colgroup id="TBL-10-2g"><col 
id="TBL-10-2"></colgroup><colgroup id="TBL-10-3g"><col 
id="TBL-10-3"></colgroup><colgroup id="TBL-10-4g"><col 
id="TBL-10-4"></colgroup><colgroup id="TBL-10-5g"><col 
id="TBL-10-5"></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-10-1-"><td  style="white-space:normal; text-align:left;" id="TBL-10-1-1"  
class="td11"><!--l. 632--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">what</span>             </td><td  style="white-space:nowrap; text-align:left;" id="TBL-10-1-2"  
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:normal; text-align:left;" id="TBL-10-1-3"  
class="td11"><!--l. 632--><p class="noindent" ><span class="lstinline"></span><span 
class="cmtt-10">val</span>           </td><td  style="white-space:normal; text-align:left;" id="TBL-10-1-4"  
class="td11"><!--l. 632--><p class="noindent" ><span 
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:normal; text-align:left;" id="TBL-10-1-5"  
class="td11"><!--l. 633--><p class="noindent" ><span 
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-10-2-"><td  style="white-space:normal; text-align:left;" id="TBL-10-2-1"  
class="td11"><!--l. 634--><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-10-2-2"  
class="td11"><span class="lstinline"></span><!--l. 634--><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:normal; text-align:left;" id="TBL-10-2-3"  
class="td11"><!--l. 635--><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>
<!--l. 635--><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:normal; text-align:left;" id="TBL-10-2-4"  
class="td11"><!--l. 636--><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:normal; text-align:left;" id="TBL-10-2-5"  
class="td11"><!--l. 637--><p class="noindent" ><span 
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>
<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 
class="cmr-10">for neglecting it.</span>
<!--l. 640--><p class="noindent" ><span 
class="cmr-10">Note  that  </span><span 
class="cmtt-10">HALO </span><span 
class="cmr-10">must  be  chosen  for  the</span>
<span 
class="cmr-10">classical  Addditive  Schwarz  smoother  and</span>
<span 
class="cmr-10">its RAS variant.</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-10-3-"><td  style="white-space:normal; text-align:left;" id="TBL-10-3-1"  
class="td11"><!--l. 642--><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-10-3-2"  
class="td11"><span class="lstinline"></span><!--l. 642--><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:normal; text-align:left;" id="TBL-10-3-3"  
class="td11"><!--l. 643--><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>
<!--l. 643--><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:normal; text-align:left;" id="TBL-10-3-4"  
class="td11"><!--l. 644--><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:normal; text-align:left;" id="TBL-10-3-5"  
class="td11"><!--l. 645--><p class="noindent" ><span 
class="cmr-10">Type of prolongation operator, for Additive</span>
<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>
<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>
<span 
class="cmr-10">neglecting them.</span>
<!--l. 648--><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>
</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-10-4-"><td  style="white-space:normal; text-align:left;" id="TBL-10-4-1"  
class="td11"><!--l. 650--><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-10-4-2"  
class="td11"><span class="lstinline"></span><!--l. 650--><p class="noindent" ><span 
class="cmtt-10">integer</span>                                                                         </td><td  style="white-space:normal; text-align:left;" id="TBL-10-4-3"  
class="td11"><!--l. 651--><p class="noindent" ><span 
class="cmr-10">Any integer</span>
<!--l. 651--><p class="noindent" ><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:normal; text-align:left;" id="TBL-10-4-4"  
class="td11"><!--l. 652--><p class="noindent" ><span 
class="cmr-10">0</span>                     </td><td  style="white-space:normal; text-align:left;" id="TBL-10-4-5"  
class="td11"><!--l. 653--><p class="noindent" ><span 
class="cmr-10">Fill-in   level   </span><span 
class="cmmi-10">p  </span><span 
class="cmr-10">of   the   incomplete   LU</span>
<span 
class="cmr-10">factorizations.</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-10-5-"><td  style="white-space:normal; text-align:left;" id="TBL-10-5-1"  
class="td11"><!--l. 654--><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-10-5-2"  
class="td11"><span class="lstinline"></span><!--l. 654--><p class="noindent" ><span 
class="cmtt-10">real</span><span 
class="cmtt-10">(</span><span 
class="cmtt-10">kind_parameter</span><span 
class="cmtt-10">)</span>                                                            </td><td  style="white-space:normal; text-align:left;" id="TBL-10-5-3"  
class="td11"><!--l. 655--><p class="noindent" ><span 
class="cmr-10">Any real</span>
<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:normal; text-align:left;" id="TBL-10-5-4"  
class="td11"><!--l. 656--><p class="noindent" ><span 
class="cmr-10">0</span>                     </td><td  style="white-space:normal; text-align:left;" id="TBL-10-5-5"  
class="td11"><!--l. 657--><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 
class="cmmi-10">p,t</span><span 
class="cmr-10">)</span>
<span 
class="cmr-10">factorization.</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-10-6-"><td  style="white-space:normal; text-align:left;" id="TBL-10-6-1"  
class="td11"><!--l. 658--><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-10-6-2"  
class="td11"><span class="lstinline"></span><!--l. 658--><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:normal; text-align:left;" id="TBL-10-6-3"  
class="td11"><!--l. 659--><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>
<!--l. 659--><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:normal; text-align:left;" id="TBL-10-6-4"  
class="td11"><!--l. 660--><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:normal; text-align:left;" id="TBL-10-6-5"  
class="td11"><!--l. 661--><p class="noindent" ><span 
class="cmr-10">Whether  MUMPS  should  be  used  as  a</span>
<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>
</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-10-7-"><td  style="white-space:normal; text-align:left;" id="TBL-10-7-1"  
class="td11"><!--l. 665--><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-10-7-2"  
class="td11"><span class="lstinline"></span><!--l. 665--><p class="noindent" ><span 
class="cmtt-10">integer</span>                                                                         </td><td  style="white-space:normal; text-align:left;" id="TBL-10-7-3"  
class="td11"><!--l. 666--><p class="noindent" ><span 
class="cmr-10">Any integer</span>
<span 
class="cmr-10">number</span>            </td><td  style="white-space:normal; text-align:left;" id="TBL-10-7-4"  
class="td11"><!--l. 667--><p class="noindent" ><span 
class="cmr-10">0</span>                     </td><td  style="white-space:normal; text-align:left;" id="TBL-10-7-5"  
class="td11"><!--l. 668--><p class="noindent" ><span 
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>
<span 
class="cmr-10">argument.</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-10-8-"><td  style="white-space:normal; text-align:left;" id="TBL-10-8-1"  
class="td11"><!--l. 670--><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-10-8-2"  
class="td11"><span class="lstinline"></span><!--l. 670--><p class="noindent" ><span 
class="cmtt-10">real</span>                                                                            </td><td  style="white-space:normal; text-align:left;" id="TBL-10-8-3"  
class="td11"><!--l. 671--><p class="noindent" ><span 
class="cmr-10">Any real number</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-10-8-4"  
class="td11"><!--l. 672--><p class="noindent" ><span 
class="cmr-10">0</span> </td><td  style="white-space:normal; text-align:left;" id="TBL-10-8-5"  
class="td11"><!--l. 673--><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>
<span 
class="cmr-10">argument.</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-10-9-"><td  style="white-space:normal; text-align:left;" id="TBL-10-9-1"  
class="td11">                  </td></tr></table></div></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;8: </span><span  
class="content">Parameters defining the smoother or the details of the one-level preconditioner
(continued).</span></div><!--tex4ht:label?: x19-18015r8 -->
                                                                               

                                                                               
   </div><hr class="endfloat" />
   </div>
                                                                               

                                                                               
                                                                               

                                                                               
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