<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html > <head><title>Method set</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <!-- html,3 --> <meta name="src" content="userhtml.tex"> <link rel="stylesheet" type="text/css" href="userhtml.css"> </head><body > <!--l. 87--><div class="crosslinks"><p class="noindent"><span class="cmr-12">[</span><a href="userhtmlsu12.html" ><span class="cmr-12">next</span></a><span class="cmr-12">] [</span><a href="userhtmlsu10.html" ><span class="cmr-12">prev</span></a><span class="cmr-12">] [</span><a href="userhtmlsu10.html#tailuserhtmlsu10.html" ><span class="cmr-12">prev-tail</span></a><span class="cmr-12">] [</span><a href="#tailuserhtmlsu11.html"><span class="cmr-12">tail</span></a><span class="cmr-12">] [</span><a href="userhtmlse6.html#userhtmlsu11.html" ><span class="cmr-12">up</span></a><span class="cmr-12">] </span></p></div> <h4 class="subsectionHead"><span class="titlemark"><span class="cmr-12">6.2 </span></span> <a id="x21-200006.2"></a><span class="cmr-12">Method set</span></h4> <div class="center" > <!--l. 89--><p class="noindent" > <!--l. 90--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">call</span><span class="cmtt-12"> p%set(what,val,info</span><span class="cmtt-12"> [,ilev,</span><span class="cmtt-12"> ilmax,</span><span class="cmtt-12"> pos,</span><span class="cmtt-12"> idx])</span></span></span></div> <!--l. 93--><p class="noindent" ><span class="cmr-12">This method sets the parameters defining the preconditioner </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">p</span></span></span><span class="cmr-12">. More precisely, the</span> <span class="cmr-12">parameter identified by </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">what</span></span></span> <span class="cmr-12">is assigned the value contained in </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">val</span></span></span><span class="cmr-12">.</span> <!--l. 98--><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:wrap; text-align:left;" id="TBL-3-1-1" class="td11"><!--l. 105--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">what</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-1-2" class="td11"><!--l. 105--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">character(len=*)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-2-"><td style="white-space:wrap; text-align:left;" id="TBL-3-2-1" class="td11"><!--l. 106--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-2-2" class="td11"><!--l. 106--><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"> </span><a href="#x21-200092"><span class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span class="cmr-12">-</span><a href="#x21-200158"><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:wrap; text-align:left;" id="TBL-3-3-1" class="td11"><!--l. 109--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">val</span><span class="cmtt-12"> </span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-3-2" class="td11"><!--l. 109--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">integer</span></span></span> <span class="cmti-12">or </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">character(len=*)</span></span></span> <span class="cmti-12">or </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">real(psb_spk_)</span></span></span> <span class="cmti-12">or</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">real(psb_dpk_)</span></span></span><span class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">intent(in)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-4-"><td style="white-space:wrap; text-align:left;" id="TBL-3-4-1" class="td11"><!--l. 112--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-4-2" class="td11"><!--l. 112--><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"> </span><a href="#x21-200092"><span class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span class="cmr-12">-</span><a href="#x21-200158"><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="obeylines-h"><span class="verb"><span class="cmtt-12">character(len=*)</span></span></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:wrap; text-align:left;" id="TBL-3-5-1" class="td11"><!--l. 117--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">info</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-5-2" class="td11"><!--l. 117--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">integer,</span><span class="cmtt-12"> intent(out)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-6-"><td style="white-space:wrap; text-align:left;" id="TBL-3-6-1" class="td11"><!--l. 118--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-6-2" class="td11"><!--l. 118--><p class="noindent" ><span class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span class="cmr-12"> </span><a href="userhtmlse8.html#x30-340008"><span class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span class="cmr-12">for details.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-7-"><td style="white-space:wrap; text-align:left;" id="TBL-3-7-1" class="td11"><!--l. 120--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilev</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-7-2" class="td11"><!--l. 120--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">integer,</span><span class="cmtt-12"> optional,</span><span class="cmtt-12"> intent(in)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-8-"><td style="white-space:wrap; text-align:left;" id="TBL-3-8-1" class="td11"><!--l. 121--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-8-2" class="td11"><!--l. 121--><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="obeylines-h"><span class="verb"><span class="cmtt-12">ilev</span></span></span> <span class="cmr-12">is not present, the parameter identified by </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">what</span></span></span> <span class="cmr-12">is set at all the appropriate levels (see Tables</span><span class="cmr-12"> </span><a href="#x21-200092"><span class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span class="cmr-12">-</span><a href="#x21-200158"><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:wrap; text-align:left;" id="TBL-3-9-1" class="td11"><!--l. 128--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilmax</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-9-2" class="td11"><!--l. 128--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">integer,</span><span class="cmtt-12"> optional,</span><span class="cmtt-12"> intent(in)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-10-"><td style="white-space:wrap; text-align:left;" id="TBL-3-10-1" class="td11"><!--l. 129--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-10-2" class="td11"><!--l. 129--><p class="noindent" ><span class="cmr-12">For the multilevel preconditioner, when both </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilev</span></span></span> <span class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilmax</span></span></span> <span class="cmr-12">are</span> <span class="cmr-12">present, the settings are applied at all levels </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilev:ilmax</span></span></span><span class="cmr-12">. When</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilev</span></span></span> <span class="cmr-12">is present but </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilmax</span></span></span> <span class="cmr-12">is not, then the default is </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilmax=ilev</span></span></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:wrap; text-align:left;" id="TBL-3-11-1" class="td11"><!--l. 136--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">pos</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-11-2" class="td11"><!--l. 136--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">charater(len=*),</span><span class="cmtt-12"> optional,</span><span class="cmtt-12"> intent(in)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-12-"><td style="white-space:wrap; text-align:left;" id="TBL-3-12-1" class="td11"><!--l. 137--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-12-2" class="td11"><!--l. 137--><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="obeylines-h"><span class="verb"><span class="cmtt-12">’PRE’</span></span></span><span class="cmr-12">) or to the post-smoother (</span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">’POST’</span></span></span><span class="cmr-12">). If </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">pos</span></span></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="obeylines-h"><span class="verb"><span class="cmtt-12">what</span></span></span> <span class="cmr-12">does</span> <span class="cmr-12">not concern the smoothers, </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">pos</span></span></span> <span class="cmr-12">is ignored.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-13-"><td style="white-space:wrap; text-align:left;" id="TBL-3-13-1" class="td11"><!--l. 142--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">idx</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-3-13-2" class="td11"><!--l. 142--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">integer,</span><span class="cmtt-12"> optional,</span><span class="cmtt-12"> intent(in)</span></span></span><span class="cmr-12">.</span> </td> </tr><tr style="vertical-align:baseline;" id="TBL-3-14-"><td style="white-space:wrap; text-align:left;" id="TBL-3-14-1" class="td11"><!--l. 143--><p class="noindent" > </td><td style="white-space:wrap; text-align:left;" id="TBL-3-14-2" class="td11"><!--l. 143--><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. 148--><p class="indent" > <span class="cmr-12">For compatibility with the previous versions of MLD2P4, this method can be also</span> <span class="cmr-12">invoked as follows:</span> <div class="center" > <!--l. 151--><p class="noindent" > <!--l. 152--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-12">call</span><span class="cmtt-12"> mld_precset(p,what,val,info)</span></span></span></div> <!--l. 155--><p class="noindent" ><span class="cmr-12">However, in this case the optional arguments </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilev</span></span></span><span class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">ilmax</span></span></span><span class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">pos</span></span></span> <span class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">idx</span></span></span> <span class="cmr-12">cannot be</span> <span class="cmr-12">used. </span><br class="newline" /> <!--l. 160--><p class="indent" > <span class="cmr-12">A variety of preconditioners can be obtained by a suitable setting of the</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="x21-20002x1"><span class="cmr-12">the type of multilevel cycle and how many cycles must be applied;</span> </li> <li class="enumerate" id="x21-20004x2"><span class="cmr-12">the aggregation algorithm;</span> </li> <li class="enumerate" id="x21-20006x3"><span class="cmr-12">the coarse-space correction at the coarsest level (for multilevel</span> <span class="cmr-12">preconditioners only);</span> </li> <li class="enumerate" id="x21-20008x4"><span class="cmr-12">the smoother of the multilevel preconditioners, or the one-level</span> <span class="cmr-12">preconditioner.</span> </li></ol> <!--l. 172--><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"> </span><a href="#x21-200092"><span class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span class="cmr-12">-</span><a href="#x21-200158"><span class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span class="cmr-12">. For a description of the meaning of the parameters, please refer</span> <span class="cmr-12">also to Section</span><span class="cmr-12"> </span><a href="userhtmlse4.html#x13-120004"><span class="cmr-12">4</span><!--tex4ht:ref: sec:background --></a><span class="cmr-12">. </span><br class="newline" /> <!--l. 177--><p class="indent" > <span class="cmbx-12">Remark 2. </span><span class="cmr-12">A smoother is usually obtained by combining two objects:</span> <span class="cmr-12">a smoother (</span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">SMOOTHER_TYPE</span></span></span><span class="cmr-12">) and a local solver (</span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">SUB_SOLVE</span></span></span><span class="cmr-12">), as specified</span> <span class="cmr-12">in Tables</span><span class="cmr-12"> </span><a href="#x21-200147"><span class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span class="cmr-12">-</span><a href="#x21-200158"><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</span> <span class="cmr-12">blocks is obtained by combining the block-Jacobi smoother object with the</span> <span class="cmr-12">ILU(0) solver object. Similarly, the hybrid Gauss-Seidel smoother (see Note in</span> <span class="cmr-12">Table</span><span class="cmr-12"> </span><a href="#x21-200147"><span class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span class="cmr-12">) is obtained by combining the block-Jacobi smoother object with a</span> <span class="cmr-12">single sweep of the Gauss-Seidel solver object, while the point-Jacobi smoother</span> <span class="cmr-12">is the result of combining the block-Jacobi smoother object with a single</span> <span class="cmr-12">sweep of the pointwise-Jacobi solver object. However, for simplicity, shortcuts</span> <span class="cmr-12">are provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and hybrid</span> <span class="cmr-12">backward Gauss-Seidel, i.e., the previous smoothers can be defined by setting only</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">SMOOTHER_TYPE</span></span></span> <span class="cmr-12">to appropriate values (see Tables</span><span class="cmr-12"> </span><a href="#x21-200147"><span class="cmr-12">7</span><!--tex4ht:ref: tab:p_smoother --></a><span class="cmr-12">), i.e., without setting </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">SUB_SOLVE</span></span></span> <span class="cmr-12">too.</span> <!--l. 194--><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. 203--><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"> </span><a href="#x21-200125"><span class="cmr-12">5</span><!--tex4ht:ref: tab:p_coarse --></a><span class="cmr-12">).</span> <br class="newline" /> <!--l. 207--><p class="indent" > <span class="cmbx-12">Remark 3. </span><span class="cmr-12">In general, a coarsest-level solver cannot be used with both the</span> <span class="cmr-12">replicated and distributed coarsest-matrix layout; therefore, setting the solver after the</span> <span class="cmr-12">layout may change the layout. Similarly, setting the layout after the solver may change</span> <span class="cmr-12">the solver.</span> <!--l. 212--><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 requires it to be distributed. In these cases, setting the</span> <span class="cmr-12">coarsest-level solver implies that the layout is redefined according to the solver,</span> <span class="cmr-12">ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel and</span> <span class="cmr-12">block-Jacobi can be applied to replicated and distributed matrices, thus their choice</span> <span class="cmr-12">does not modify any previously specified layout. It is worth noting that, when the</span> <span class="cmr-12">matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi</span> <span class="cmr-12">solvers reduce to the corresponding local solver objects (see Remark</span><span class="cmr-12"> 2). For the</span> <span class="cmr-12">point-Jacobi and Gauss-Seidel solvers, these objects correspond to a </span><span class="cmti-12">single</span> <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. 227--><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</span> <span class="cmr-12">chosen solver applied to the local blocks. Likewise, the replicated layout can be</span> <span class="cmr-12">used with any solver but SuperLu</span><span class="cmr-12">_Dist; therefore, if SuperLu</span><span class="cmr-12">_Dist has been</span> <span class="cmr-12">previously set, the coarsest-level solver is changed to the default sequential</span> <span class="cmr-12">solver.</span> <!--l. 235--><p class="indent" > <span class="cmbx-12">Remark 4. </span><span class="cmr-12">The argument </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">idx</span></span></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="obeylines-h"><span class="verb"><span class="cmtt-12">MUMPS_IPAR_ENTRY</span></span></span> <span class="cmr-12">and an appropriate value</span> <span class="cmr-12">for </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">idx</span></span></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"> </span><a href="userhtmlse7.html#x29-330007"><span class="cmr-12">7</span><!--tex4ht:ref: sec:adding --></a><span class="cmr-12">.</span> <div class="table"> <!--l. 246--><p class="indent" > <a id="x21-200092"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 246--><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:wrap; text-align:left;" id="TBL-4-1-1" class="td11"><!--l. 250--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">what</span></span></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:wrap; text-align:left;" id="TBL-4-1-3" class="td11"><!--l. 250--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-1-4" class="td11"><!--l. 250--><p class="noindent" ><span class="cmcsc-10x-x-109"><span class="small-caps">d</span><span class="small-caps">e</span><span class="small-caps">f</span><span class="small-caps">a</span><span class="small-caps">u</span><span class="small-caps">l</span><span class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-1-5" class="td11"><!--l. 251--><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:wrap; text-align:left;" id="TBL-4-2-1" class="td11"><!--l. 254--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’ML_CYCLE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-4-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-3" class="td11"><!--l. 255--><p class="noindent" ><span class="cmtt-10x-x-109">’VCYCLE’</span> <!--l. 255--><p class="noindent" ><span class="cmtt-10x-x-109">’WCYCLE’</span> <!--l. 255--><p class="noindent" ><span class="cmtt-10x-x-109">’KCYCLE’</span> <!--l. 256--><p class="noindent" ><span class="cmtt-10x-x-109">’MULT’</span> <!--l. 256--><p class="noindent" ><span class="cmtt-10x-x-109">’ADD’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-4" class="td11"><!--l. 257--><p class="noindent" ><span class="cmtt-10x-x-109">’VCYCLE’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-4-2-5" class="td11"><!--l. 258--><p class="noindent" >Multilevel cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz, and Additive Schwarz. <!--l. 260--><p class="noindent" >Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and is included for compatibility with previous versions of MLD2P4. </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-4-3-"><td style="white-space:wrap; text-align:left;" id="TBL-4-3-1" class="td11"><!--l. 263--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’OUTER_SWEEPS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-4-3-2" class="td11"><span class="cmtt-10x-x-109">integer </span></td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-3" class="td11"><!--l. 264--><p class="noindent" >Any integer <!--l. 264--><p class="noindent" >number <span class="cmsy-10x-x-109">≥ </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-4" class="td11"><!--l. 264--><p class="noindent" >1 </td><td style="white-space:wrap; text-align:left;" id="TBL-4-3-5" class="td11"><!--l. 265--><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:wrap; text-align:left;" id="TBL-4-4-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 2: </span><span class="content">Parameters defining the multilevel cycle and the number of cycles to be applied. </span></div><!--tex4ht:label?: x21-200092 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 285--><p class="indent" > <a id="x21-200103"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 285--><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:wrap; text-align:left;" id="TBL-5-1-1" class="td11"><!--l. 289--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">what</span></span></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:wrap; text-align:left;" id="TBL-5-1-3" class="td11"><!--l. 289--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-1-4" class="td11"><!--l. 289--><p class="noindent" ><span class="cmcsc-10x-x-109"><span class="small-caps">d</span><span class="small-caps">e</span><span class="small-caps">f</span><span class="small-caps">a</span><span class="small-caps">u</span><span class="small-caps">l</span><span class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-1-5" class="td11"><!--l. 290--><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:wrap; text-align:left;" id="TBL-5-2-1" class="td11"><!--l. 293--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’MIN_COARSE_SIZE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-3" class="td11"><!--l. 294--><p class="noindent" >Any number <!--l. 294--><p class="noindent" ><span class="cmmi-10x-x-109">> </span>0 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-4" class="td11"><!--l. 295--><p class="noindent" ><span class="cmsy-10x-x-109">⌊</span>40<img src="userhtml19x.png" alt="√ -- 3 n" class="root" align="middle" ><span class="cmsy-10x-x-109">⌋</span>, where <span class="cmmi-10x-x-109">n</span> is the dimension of the matrix at the finest level </td><td style="white-space:wrap; text-align:left;" id="TBL-5-2-5" class="td11"><!--l. 297--><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).</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:wrap; text-align:left;" id="TBL-5-3-1" class="td11"><!--l. 309--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’MIN_CR_RATIO’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">real</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-3" class="td11"><!--l. 310--><p class="noindent" >Any number <!--l. 310--><p class="noindent" ><span class="cmmi-10x-x-109">> </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-4" class="td11"><!--l. 311--><p class="noindent" >1.5 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-3-5" class="td11"><!--l. 312--><p class="noindent" >Minimum coarsening ratio. The aggregation stops if the ratio between the 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-5-4-"><td style="white-space:wrap; text-align:left;" id="TBL-5-4-1" class="td11"><!--l. 317--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’MAX_LEVS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-3" class="td11"><!--l. 318--><p class="noindent" >Any integer <!--l. 318--><p class="noindent" >number <span class="cmmi-10x-x-109">> </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-4" class="td11"><!--l. 319--><p class="noindent" >20 </td><td style="white-space:wrap; text-align:left;" id="TBL-5-4-5" class="td11"><!--l. 320--><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-5-5-"><td style="white-space:wrap; text-align:left;" id="TBL-5-5-1" class="td11"><!--l. 323--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’PAR_AGGR_ALG’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-5-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-3" class="td11"><!--l. 324--><p class="noindent" ><span class="cmtt-10x-x-109">’DEC’</span>, <span class="cmtt-10x-x-109">’SYMDEC’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-4" class="td11"><!--l. 325--><p class="noindent" ><span class="cmtt-10x-x-109">’DEC’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-5-5" class="td11"><!--l. 326--><p class="noindent" >Parallel aggregation algorithm. <!--l. 326--><p class="noindent" >Currently, only the decoupled aggregation (<span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">DEC</span></span></span>) is available; the <span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">SYMDEC</span></span></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-5-6-"><td style="white-space:wrap; text-align:left;" id="TBL-5-6-1" class="td11"><!--l. 332--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’AGGR_TYPE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-6-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-3" class="td11"><!--l. 333--><p class="noindent" ><span class="cmtt-10x-x-109">’SOC1’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-4" class="td11"><!--l. 334--><p class="noindent" ><span class="cmtt-10x-x-109">’SOC1’</span>, <span class="cmtt-10x-x-109">’SOC2’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-6-5" class="td11"><!--l. 336--><p class="noindent" >Type of aggregation algorithm: currently, we implement to measures of strength of connection, the one by Vaněk, Mandel and Brezina <span class="cite">[<a href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">26</a>]</span>, and the one by Gratton et al <span class="cite">[<a href="userhtmlli4.html#XGrHeJi:16">16</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-5-7-"><td style="white-space:wrap; text-align:left;" id="TBL-5-7-1" class="td11"><!--l. 342--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’AGGR_PROL’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-5-7-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-3" class="td11"><!--l. 343--><p class="noindent" ><span class="cmtt-10x-x-109">’SMOOTHED’</span>, <span class="cmtt-10x-x-109">’UNSMOOTHED’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-4" class="td11"><!--l. 343--><p class="noindent" ><span class="cmtt-10x-x-109">’SMOOTHED’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-5-7-5" class="td11"><!--l. 344--><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-5-8-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-8-1" 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, the</div> </tr><tr style="vertical-align:baseline;" id="TBL-5-9-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-9-1" class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">minimum coarsening ratio, or the maximum number of levels is reached. Therefore, the actual number of levels may be</div> </tr><tr style="vertical-align:baseline;" id="TBL-5-10-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-5-10-1" class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">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-5-11-"><td style="white-space:wrap; text-align:left;" id="TBL-5-11-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 3: </span><span class="content">Parameters defining the aggregation algorithm. </span></div><!--tex4ht:label?: x21-200103 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 362--><p class="indent" > <a id="x21-200114"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 362--><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:wrap; text-align:left;" id="TBL-6-1-1" class="td11"><!--l. 366--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">what</span></span></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:wrap; text-align:left;" id="TBL-6-1-3" class="td11"><!--l. 366--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-1-4" class="td11"><!--l. 366--><p class="noindent" ><span class="cmcsc-10x-x-109"><span class="small-caps">d</span><span class="small-caps">e</span><span class="small-caps">f</span><span class="small-caps">a</span><span class="small-caps">u</span><span class="small-caps">l</span><span class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-1-5" class="td11"><!--l. 367--><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:wrap; text-align:left;" id="TBL-6-2-1" class="td11"><!--l. 369--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’AGGR_ORD’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-3" class="td11"><!--l. 370--><p class="noindent" ><span class="cmtt-10x-x-109">’NATURAL’</span> <!--l. 370--><p class="noindent" ><span class="cmtt-10x-x-109">’DEGREE’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-4" class="td11"><!--l. 371--><p class="noindent" ><span class="cmtt-10x-x-109">’NATURAL’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-2-5" class="td11"><!--l. 372--><p class="noindent" >Initial ordering of indices for the aggregation algorithm: either natural ordering or sorted by descending degrees of the nodes in the matrix graph. </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-6-3-"><td style="white-space:wrap; text-align:left;" id="TBL-6-3-1" class="td11"><!--l. 379--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’AGGR_THRESH’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">real(</span></span></span><span class="cmti-10x-x-109">kind</span><span class="cmti-10x-x-109">_parameter</span><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-3" class="td11"><!--l. 380--><p class="noindent" >Any real <!--l. 380--><p class="noindent" >number <span class="cmsy-10x-x-109">∈</span> [0<span class="cmmi-10x-x-109">,</span>1] </td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-4" class="td11"><!--l. 381--><p class="noindent" >0.01 </td><td style="white-space:wrap; text-align:left;" id="TBL-6-3-5" class="td11"><!--l. 382--><p class="noindent" >The threshold <span class="cmmi-10x-x-109">θ </span>in the aggregation algorithm, see (<a href="userhtmlsu7.html#x15-14007r3">3<!--tex4ht:ref: eq:strongly_coup --></a>) in Section <a href="userhtmlsu7.html#x15-140004.2">4.2<!--tex4ht:ref: sec:aggregation --></a>. See also the note at the bottom of this table.</td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-6-4-"><td style="white-space:wrap; text-align:left;" id="TBL-6-4-1" class="td11"><!--l. 421--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’AGGR_FILTER’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-6-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-3" class="td11"><!--l. 423--><p class="noindent" ><span class="cmtt-10x-x-109">’FILTER’</span> <!--l. 423--><p class="noindent" ><span class="cmtt-10x-x-109">’NOFILTER’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-4" class="td11"><!--l. 424--><p class="noindent" ><span class="cmtt-10x-x-109">’NOFILTER’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-6-4-5" class="td11"><!--l. 424--><p class="noindent" >Matrix used in computing the smoothed prolongator: filtered or unfiltered (see (<a href="userhtmlsu7.html#x15-14009r5">5<!--tex4ht:ref: eq:filtered --></a>) in Section <a href="userhtmlsu7.html#x15-140004.2">4.2<!--tex4ht:ref: sec:aggregation --></a>). </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-6-5-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-6-5-1" class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;"><span class="cmbx-10x-x-109">Note. </span>Different thresholds at different levels, such as those used in <span class="cite">[<a href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">26</a>, Section 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:wrap; 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:wrap; text-align:left;" id="TBL-6-7-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 4: </span><span class="content">Parameters defining the aggregation algorithm (continued). </span></div><!--tex4ht:label?: x21-200114 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 440--><p class="indent" > <a id="x21-200125"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 440--><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:wrap; text-align:left;" id="TBL-7-1-1" class="td11"><!--l. 443--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">what</span></span></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:wrap; text-align:left;" id="TBL-7-1-3" class="td11"><!--l. 443--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-1-4" class="td11"><!--l. 443--><p class="noindent" ><span class="cmcsc-10x-x-109"><span class="small-caps">d</span><span class="small-caps">e</span><span class="small-caps">f</span><span class="small-caps">a</span><span class="small-caps">u</span><span class="small-caps">l</span><span class="small-caps">t</span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-1-5" class="td11"><!--l. 444--><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:wrap; text-align:left;" id="TBL-7-2-1" class="td11"><!--l. 447--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_MAT’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-3" class="td11"><!--l. 448--><p class="noindent" ><span class="cmtt-10x-x-109">’DIST’</span> <!--l. 448--><p class="noindent" ><span class="cmtt-10x-x-109">’REPL’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-4" class="td11"><!--l. 449--><p class="noindent" ><span class="cmtt-10x-x-109">’REPL’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-2-5" class="td11"><!--l. 450--><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:wrap; text-align:left;" id="TBL-7-3-1" class="td11"><!--l. 453--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_SOLVE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-3" class="td11"><!--l. 454--><p class="noindent" ><span class="cmtt-10x-x-109">’MUMPS’</span> <!--l. 454--><p class="noindent" ><span class="cmtt-10x-x-109">’UMF’</span> <!--l. 455--><p class="noindent" ><span class="cmtt-10x-x-109">’SLU’</span> <!--l. 455--><p class="noindent" ><span class="cmtt-10x-x-109">’SLUDIST’</span> <!--l. 456--><p class="noindent" ><span class="cmtt-10x-x-109">’JACOBI’</span> <!--l. 456--><p class="noindent" ><span class="cmtt-10x-x-109">’GS’</span> <!--l. 456--><p class="noindent" ><span class="cmtt-10x-x-109">’BJAC’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-4" class="td11"><!--l. 457--><p class="noindent" >See Note.</td><td style="white-space:wrap; text-align:left;" id="TBL-7-3-5" class="td11"><!--l. 458--><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. <!--l. 464--><p class="noindent" >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>and <span class="cmtt-10x-x-109">BJAC</span> require it to be distributed, and <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. 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:wrap; text-align:left;" id="TBL-7-4-1" class="td11"><!--l. 474--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_SUBSOLVE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-7-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-3" class="td11"><!--l. 475--><p class="noindent" ><span class="cmtt-10x-x-109">’ILU’</span> <!--l. 475--><p class="noindent" ><span class="cmtt-10x-x-109">’ILUT’</span> <!--l. 475--><p class="noindent" ><span class="cmtt-10x-x-109">’MILU’</span> <!--l. 476--><p class="noindent" ><span class="cmtt-10x-x-109">’MUMPS’</span> <!--l. 476--><p class="noindent" ><span class="cmtt-10x-x-109">’SLU’</span> <!--l. 476--><p class="noindent" ><span class="cmtt-10x-x-109">’UMF’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-4" class="td11"><!--l. 477--><p class="noindent" >See Note.</td><td style="white-space:wrap; text-align:left;" id="TBL-7-4-5" class="td11"><!--l. 478--><p class="noindent" >Solver for the diagonal blocks of the coarse 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). 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:wrap; 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:wrap; text-align:left;" id="TBL-7-6-1" class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">single precision version – <span class="cmtt-10x-x-109">MUMPS </span>if installed, then <span class="cmtt-10x-x-109">SLU </span>if installed, <span class="cmtt-10x-x-109">ILU </span>otherwise;</div> </tr><tr style="vertical-align:baseline;" id="TBL-7-7-"><td colspan="3" style="white-space:wrap; text-align:left;" id="TBL-7-7-1" class="td11"></td><div class="multicolumn" style="white-space:nowrap; text-align:left;">double precision version – <span class="cmtt-10x-x-109">UMF </span>if installed, then <span class="cmtt-10x-x-109">MUMPS </span>if installed, then <span class="cmtt-10x-x-109">SLU </span>if installed, <span class="cmtt-10x-x-109">ILU </span>otherwise.</div> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-7-8-"><td style="white-space:wrap; text-align:left;" id="TBL-7-8-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 5: </span><span class="content">Parameters defining the coarse-space correction at the coarsest level.</span></div><!--tex4ht:label?: x21-200125 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 502--><p class="indent" > <a id="x21-200136"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 502--><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:wrap; text-align:left;" id="TBL-8-1-1" class="td11"><!--l. 505--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">what</span></span></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:wrap; text-align:left;" id="TBL-8-1-3" class="td11"><!--l. 505--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-1-4" class="td11"><!--l. 505--><p class="noindent" ><span class="cmcsc-10x-x-109"><span class="small-caps">d</span><span class="small-caps">e</span><span class="small-caps">f</span><span class="small-caps">a</span><span class="small-caps">u</span><span class="small-caps">l</span><span class="small-caps">t</span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-8-1-5" class="td11"><!--l. 506--><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:wrap; text-align:left;" id="TBL-8-2-1" class="td11"><!--l. 509--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_SWEEPS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-3" class="td11"><!--l. 510--><p class="noindent" >Any integer <!--l. 510--><p class="noindent" >number <span class="cmmi-10x-x-109">> </span>0</td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-4" class="td11"><!--l. 511--><p class="noindent" >10 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-2-5" class="td11"><!--l. 512--><p class="noindent" >Number of sweeps when <span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">JACOBI</span></span></span>, <span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">GS</span></span></span> or <span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">BJAC</span></span></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-8-3-"><td style="white-space:wrap; text-align:left;" id="TBL-8-3-1" class="td11"><!--l. 515--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_FILLIN’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-3" class="td11"><!--l. 516--><p class="noindent" >Any integer <!--l. 516--><p class="noindent" >number <span class="cmsy-10x-x-109">≥ </span>0</td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-4" class="td11"><!--l. 517--><p class="noindent" >0 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-3-5" class="td11"><!--l. 518--><p class="noindent" >Fill-in level <span class="cmmi-10x-x-109">p </span>of the ILU factorizations. </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-8-4-"><td style="white-space:wrap; text-align:left;" id="TBL-8-4-1" class="td11"><!--l. 520--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">’COARSE_ILUTHRS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-8-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">real(</span></span></span><span class="cmti-10x-x-109">kind</span><span class="cmti-10x-x-109">_parameter</span><span class="obeylines-h"><span class="verb"><span class="cmtt-10x-x-109">)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-3" class="td11"><!--l. 522--><p class="noindent" >Any real <!--l. 522--><p class="noindent" >number <span class="cmsy-10x-x-109">≥ </span>0</td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-4" class="td11"><!--l. 523--><p class="noindent" >0 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-5" class="td11"><!--l. 524--><p class="noindent" >Drop tolerance <span class="cmmi-10x-x-109">t </span>in the ILU(<span class="cmmi-10x-x-109">p,t</span>) factorization. </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-8-5-"><td style="white-space:wrap; text-align:left;" id="TBL-8-5-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 6: </span><span class="content">Parameters defining the coarse-space correction at the coarsest level (continued).</span></div><!--tex4ht:label?: x21-200136 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 533--><p class="indent" > <a id="x21-200147"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 533--><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:wrap; text-align:left;" id="TBL-9-1-1" class="td11"><!--l. 537--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">what</span></span></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:wrap; text-align:left;" id="TBL-9-1-3" class="td11"><!--l. 537--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-1-4" class="td11"><!--l. 537--><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:wrap; text-align:left;" id="TBL-9-1-5" class="td11"><!--l. 538--><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:wrap; text-align:left;" id="TBL-9-2-1" class="td11"><!--l. 541--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SMOOTHER_TYPE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-3" class="td11"><!--l. 542--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’JACOBI’</span></span></span> <!--l. 542--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’GS’</span></span></span> <!--l. 542--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’BGS’</span></span></span> <!--l. 542--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’BJAC’</span></span></span> <!--l. 543--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’AS’</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-4" class="td11"><!--l. 544--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’FBGS’</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-2-5" class="td11"><!--l. 545--><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, and Additive</span> <span class="cmr-10">Schwarz.</span> <!--l. 549--><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:wrap; text-align:left;" id="TBL-9-3-1" class="td11"><!--l. 551--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_SOLVE’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">character(len=*)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-9-3-3" class="td11"><!--l. 552--><p class="noindent" ><span class="cmtt-10">’JACOBI’</span> <!--l. 553--><p class="noindent" ><span class="cmtt-10">’GS’</span> <!--l. 553--><p class="noindent" ><span class="cmtt-10">’BGS’</span> <!--l. 553--><p class="noindent" ><span class="cmtt-10">’ILU’</span> <!--l. 554--><p class="noindent" ><span class="cmtt-10">’ILUT’</span> <!--l. 554--><p class="noindent" ><span class="cmtt-10">’MILU’</span> <!--l. 555--><p class="noindent" ><span class="cmtt-10">’MUMPS’</span> <!--l. 555--><p class="noindent" ><span class="cmtt-10">’SLU’</span> <!--l. 555--><p class="noindent" ><span class="cmtt-10">’UMF’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-3-4" class="td11"><!--l. 556--><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. 558--><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:wrap; text-align:left;" id="TBL-9-3-5" class="td11"><!--l. 560--><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"> 2, page</span><span class="cmr-10"> 24): point-Jacobi, hybrid</span> <span class="cmr-10">(forward) Gauss-Seidel, hybrid backward</span> <span class="cmr-10">Gauss-Seidel, ILU(</span><span class="cmmi-10">p</span><span class="cmr-10">), ILU(</span><span class="cmmi-10">p,t</span><span class="cmr-10">), MILU(</span><span class="cmmi-10">p</span><span class="cmr-10">),</span> <span class="cmr-10">LU from MUMPS, SuperLU</span> <span class="cmr-10">or UMFPACK (plus triangular solve). See</span> <span class="cmr-10">Note for details on hybrid Gauss-Seidel.</span> </td> </tr><tr class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr style="vertical-align:baseline;" id="TBL-9-4-"><td style="white-space:wrap; text-align:left;" id="TBL-9-4-1" class="td11"><!--l. 568--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SMOOTHER_SWEEPS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-3" class="td11"><!--l. 569--><p class="noindent" ><span class="cmr-10">Any integer</span> <!--l. 569--><p class="noindent" ><span class="cmr-10">number</span><span class="cmr-10"> </span><span class="cmsy-10">≥ </span><span class="cmr-10">0</span></td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-4" class="td11"><!--l. 570--><p class="noindent" ><span class="cmr-10">1</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-4-5" class="td11"><!--l. 571--><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="obeylines-h"><span class="verb"><span class="cmtt-10">pos=’PRE’</span></span></span> <span class="cmr-10">or </span><span class="obeylines-h"><span class="verb"><span class="cmtt-10">pos=’POST</span></span></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:wrap; text-align:left;" id="TBL-9-5-1" class="td11"><!--l. 577--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_OVR’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-9-5-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-3" class="td11"><!--l. 578--><p class="noindent" ><span class="cmr-10">Any integer</span> <!--l. 578--><p class="noindent" ><span class="cmr-10">number</span><span class="cmr-10"> </span><span class="cmsy-10">≥ </span><span class="cmr-10">0</span></td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-4" class="td11"><!--l. 579--><p class="noindent" ><span class="cmr-10">1</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-9-5-5" class="td11"><!--l. 580--><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:wrap; text-align:left;" id="TBL-9-6-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 7: </span><span class="content">Parameters defining the smoother or the details of the one-level preconditioner. </span></div><!--tex4ht:label?: x21-200147 --> </div><hr class="endfloat" /> </div> <div class="table"> <!--l. 589--><p class="indent" > <a id="x21-200158"></a><hr class="float"><div class="float" > <div class="center" > <!--l. 589--><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:wrap; text-align:left;" id="TBL-10-1-1" class="td11"><!--l. 593--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">what</span></span></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:wrap; text-align:left;" id="TBL-10-1-3" class="td11"><!--l. 593--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">val</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-1-4" class="td11"><!--l. 593--><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:wrap; text-align:left;" id="TBL-10-1-5" class="td11"><!--l. 594--><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:wrap; text-align:left;" id="TBL-10-2-1" class="td11"><!--l. 596--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_RESTR’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-2-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">character(len=*)</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-2-3" class="td11"><!--l. 597--><p class="noindent" ><span class="cmtt-10">’HALO’</span> <!--l. 597--><p class="noindent" ><span class="cmtt-10">’NONE’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-2-4" class="td11"><!--l. 598--><p class="noindent" ><span class="cmtt-10">’HALO’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-2-5" class="td11"><!--l. 599--><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 the</span> <span class="cmr-10">overlap, </span><span class="cmtt-10">NONE </span><span class="cmr-10">for neglecting it.</span> <!--l. 602--><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 classical</span> <span class="cmr-10">Addditive Schwarz smoother and its RAS</span> <span class="cmr-10">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:wrap; text-align:left;" id="TBL-10-3-1" class="td11"><!--l. 605--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_PROL’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-3-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">character(len=*)</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-3-3" class="td11"><!--l. 606--><p class="noindent" ><span class="cmtt-10">’SUM’</span> <!--l. 606--><p class="noindent" ><span class="cmtt-10">’NONE’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-3-4" class="td11"><!--l. 607--><p class="noindent" ><span class="cmtt-10">’NONE’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-3-5" class="td11"><!--l. 608--><p class="noindent" ><span class="cmr-10">Type of prolongation operator, for Additive</span> <span class="cmr-10">Schwarz only: </span><span class="cmtt-10">SUM </span><span class="cmr-10">for adding the contributions</span> <span class="cmr-10">from the overlap, </span><span class="cmtt-10">NONE </span><span class="cmr-10">for neglecting them.</span> <!--l. 611--><p class="noindent" ><span class="cmr-10">Note that </span><span class="cmtt-10">SUM </span><span class="cmr-10">must be chosen for the classical</span> <span class="cmr-10">Additive Schwarz smoother, and </span><span class="cmtt-10">NONE </span><span class="cmr-10">for its</span> <span class="cmr-10">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:wrap; text-align:left;" id="TBL-10-4-1" class="td11"><!--l. 614--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_FILLIN’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-4-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-4-3" class="td11"><!--l. 615--><p class="noindent" ><span class="cmr-10">Any integer</span> <!--l. 615--><p class="noindent" ><span class="cmr-10">number</span><span class="cmr-10"> </span><span class="cmsy-10">≥ </span><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-4-4" class="td11"><!--l. 616--><p class="noindent" ><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-4-5" class="td11"><!--l. 617--><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:wrap; text-align:left;" id="TBL-10-5-1" class="td11"><!--l. 619--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’SUB_ILUTHRS’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-5-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">real(</span></span></span><span class="cmti-10">kind</span><span class="cmti-10">_parameter</span><span class="obeylines-h"><span class="verb"><span class="cmtt-10">)</span></span></span></td><td style="white-space:wrap; text-align:left;" id="TBL-10-5-3" class="td11"><!--l. 620--><p class="noindent" ><span class="cmr-10">Any real</span> <span class="cmr-10">number</span><span class="cmr-10"> </span><span class="cmsy-10">≥ </span><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-5-4" class="td11"><!--l. 621--><p class="noindent" ><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-5-5" class="td11"><!--l. 622--><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">) factorization.</span></td> </tr><tr style="vertical-align:baseline;" id="TBL-10-6-"><td style="white-space:wrap; text-align:left;" id="TBL-10-6-1" class="td11"><!--l. 623--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’MUMPS_LOC_GLOB’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-6-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">character(len=*)</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-6-3" class="td11"><!--l. 624--><p class="noindent" ><span class="cmtt-10">LOCAL</span><span class="cmtt-10">_SOLVER’</span> <!--l. 624--><p class="noindent" ><span class="cmtt-10">GLOBAL</span><span class="cmtt-10">_SOLVER’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-6-4" class="td11"><!--l. 625--><p class="noindent" ><span class="cmtt-10">GLOBAL</span><span class="cmtt-10">_SOLVER’</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-6-5" class="td11"><!--l. 626--><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 style="vertical-align:baseline;" id="TBL-10-7-"><td style="white-space:wrap; text-align:left;" id="TBL-10-7-1" class="td11"><!--l. 630--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’MUMPS_IPAR_ENTRY’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-7-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">integer</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-7-3" class="td11"><!--l. 631--><p class="noindent" ><span class="cmr-10">Any integer</span> <span class="cmr-10">number</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-7-4" class="td11"><!--l. 632--><p class="noindent" ><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-7-5" class="td11"><!--l. 633--><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="obeylines-h"><span class="verb"><span class="cmtt-10">idx</span></span></span> <span class="cmr-10">optional argument.</span></td> </tr><tr style="vertical-align:baseline;" id="TBL-10-8-"><td style="white-space:wrap; text-align:left;" id="TBL-10-8-1" class="td11"><!--l. 635--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span class="cmtt-10">’MUMPS_RPAR_ENTRY’</span></span></span> </td><td style="white-space:nowrap; text-align:left;" id="TBL-10-8-2" class="td11"><span class="obeylines-h"><span class="verb"><span class="cmtt-10">real</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-8-3" class="td11"><!--l. 636--><p class="noindent" ><span class="cmr-10">Any real</span> <span class="cmr-10">number</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-8-4" class="td11"><!--l. 637--><p class="noindent" ><span class="cmr-10">0</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-10-8-5" class="td11"><!--l. 638--><p class="noindent" ><span class="cmr-10">Set an entry in the MUMPS real control array,</span> <span class="cmr-10">as chosen via the </span><span class="obeylines-h"><span class="verb"><span class="cmtt-10">idx</span></span></span> <span class="cmr-10">optional 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:wrap; text-align:left;" id="TBL-10-9-1" class="td11"> </td></tr></table></div></div> <br /> <div class="caption" ><span class="id">Table 8: </span><span class="content">Parameters defining the smoother or the details of the one-level preconditioner (continued).</span></div><!--tex4ht:label?: x21-200158 --> </div><hr class="endfloat" /> </div> <!--l. 662--><div class="crosslinks"><p class="noindent"><span class="cmr-12">[</span><a href="userhtmlsu12.html" ><span class="cmr-12">next</span></a><span class="cmr-12">] [</span><a href="userhtmlsu10.html" ><span class="cmr-12">prev</span></a><span class="cmr-12">] [</span><a href="userhtmlsu10.html#tailuserhtmlsu10.html" ><span class="cmr-12">prev-tail</span></a><span class="cmr-12">] [</span><a href="userhtmlsu11.html" ><span class="cmr-12">front</span></a><span class="cmr-12">] [</span><a href="userhtmlse6.html#userhtmlsu11.html" ><span class="cmr-12">up</span></a><span class="cmr-12">] </span></p></div> <!--l. 662--><p class="indent" > <a id="tailuserhtmlsu11.html"></a> </body></html>