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<!-- l. 73 --> < 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
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class="cmr-12">prev-tail< / span > < / a > < span
class="cmr-12">] [< / span > < a
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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. 75 --> < p class = "noindent" >
<!-- l. 76 --> < 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. 79 --> < 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. 84 --> < 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. 87 --> < 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. 87 --> < 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. 88 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-2-2"
class="td11"><!-- l. 88 --> < 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. 91 --> < 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. 91 --> < 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. 94 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-4-2"
class="td11"><!-- l. 94 --> < 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. 99 --> < 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. 99 --> < 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. 100 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-6-2"
class="td11"><!-- l. 100 --> < 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. 102 --> < 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. 102 --> < 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. 103 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-8-2"
class="td11"><!-- l. 103 --> < 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. 110 --> < 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. 110 --> < 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. 111 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-10-2"
class="td11"><!-- l. 111 --> < 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. 118 --> < 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. 118 --> < 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. 119 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-12-2"
class="td11"><!-- l. 119 --> < 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. 124 --> < 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. 124 --> < 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. 125 --> < p class = "noindent" > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-3-14-2"
class="td11"><!-- l. 125 --> < 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. 130 --> < 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. 135 --> < 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. 147 --> < 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. 152 --> < 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. 169 --> < 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. 178 --> < 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. 182 --> < 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. 187 --> < 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. 202 --> < 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. 210 --> < 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. 221 --> < p class = "indent" > < a
id="x21-200092">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 221 --> < 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. 225 --> < 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. 225 --> < 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. 225 --> < 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. 226 --> < 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. 227 --> < 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. 228 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ VCYCLE’ < / span >
<!-- l. 228 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ WCYCLE’ < / span >
<!-- l. 228 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ KCYCLE’ < / span >
<!-- l. 228 --> < 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. 229 --> < 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. 230 --> < 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:wrap; text-align:left;" id = "TBL-4-3-1"
class="td11"><!-- l. 231 --> < 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. 232 --> < p class = "noindent" > Any integer
<!-- l. 232 --> < 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. 232 --> < p class = "noindent" > 1 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-4-3-5"
class="td11"><!-- l. 233 --> < 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. 243 --> < p class = "indent" > < a
id="x21-200103">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 243 --> < 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. 247 --> < 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. 247 --> < 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. 247 --> < 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. 248 --> < 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. 249 --> < 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. 250 --> < p class = "noindent" > Any number
<!-- l. 250 --> < 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. 251 --> < 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. 253 --> < 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).
<!-- l. 259 --> < p class = "noindent" > < / 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. 261 --> < 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. 262 --> < p class = "noindent" > Any number
<!-- l. 262 --> < 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. 263 --> < p class = "noindent" > 1.5 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-5-3-5"
class="td11"><!-- l. 264 --> < 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. 269 --> < 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. 270 --> < p class = "noindent" > Any integer
<!-- l. 270 --> < 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. 271 --> < p class = "noindent" > 20 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-5-4-5"
class="td11"><!-- l. 272 --> < 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. 275 --> < 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. 276 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ DEC’ < / span > ,
< span
class="cmtt-10x-x-109">’ SYMDEC’ < / span > ,
< span
class="cmtt-10x-x-109">’ COUPLED’ < / span > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-5-5-4"
class="td11"><!-- l. 277 --> < 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. 278 --> < p class = "noindent" > Parallel aggregation algorithm.
<!-- l. 278 --> < 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. 284 --> < 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. 285 --> < 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. 286 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SOC1’ < / span > , < span
class="cmtt-10x-x-109">’ SOC2’ < / span > ,
< span
class="cmtt-10x-x-109">’ MATCHBOXP’ < / span > < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-5-6-5"
class="td11"><!-- l. 289 --> < p class = "noindent" > Type of aggregation algorithm: currently,
we implement to measures of strength of
connection, the one by Vaně k, Mandel
and Brezina  < span class = "cite" > [< a
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">28< / a > ]< / span > , and the one by Gratton
et al  < span class = "cite" > [< a
href="userhtmlli4.html#XGrHeJi:16">18< / 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. 295 --> < 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. 296 --> < 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. 296 --> < 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. 297 --> < 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 = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-5-8-1"
class="td11">< 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 >
< / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-9-">< td colspan = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-5-9-1"
class="td11">< 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 >
< / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-10-">< td colspan = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-5-10-1"
class="td11">< div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > smaller than the specified maximum number of levels. < / div >
< / 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-5-11-">< 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. 315 --> < p class = "indent" > < a
id="x21-200114">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 315 --> < 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. 319 --> < 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. 319 --> < 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. 319 --> < 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. 320 --> < 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. 322 --> < 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. 323 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ NATURAL’ < / span >
<!-- l. 323 --> < 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. 324 --> < 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. 325 --> < 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. 332 --> < 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. 333 --> < p class = "noindent" > Any  real
<!-- l. 333 --> < 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. 334 --> < p class = "noindent" > 0.01 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-6-3-5"
class="td11"><!-- l. 335 --> < 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. 338 --> < 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. 340 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ FILTER’ < / span >
<!-- l. 340 --> < 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. 341 --> < 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. 341 --> < 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 = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-6-5-1"
class="td11">< 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">28< / a > , Section  5.1]< / span > , can be easily set by invoking the rou-< / div >
< / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-6-">< td colspan = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-6-6-1"
class="td11">< 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 >
< / 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-6-7-">< 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. 357 --> < p class = "indent" > < a
id="x21-200125">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 357 --> < 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. 360 --> < 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. 360 --> < 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. 360 --> < 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. 361 --> < 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. 362 --> < 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. 363 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ DIST’ < / span >
<!-- l. 363 --> < 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. 364 --> < 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. 365 --> < 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. 367 --> < 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. 368 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MUMPS’ < / span >
<!-- l. 368 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ UMF’ < / span >
<!-- l. 369 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLU’ < / span >
<!-- l. 369 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLUDIST’ < / span >
<!-- l. 370 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ JACOBI’ < / span >
<!-- l. 370 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ GS’ < / span >
<!-- l. 370 --> < 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. 371 --> < p class = "noindent" > See  Note.< / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-7-3-5"
class="td11"><!-- l. 372 --> < 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. 378 --> < 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. 387 --> < 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. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ ILU’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ ILUT’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MILU’ < / span >
<!-- l. 389 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MUMPS’ < / span >
<!-- l. 389 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLU’ < / span >
<!-- l. 389 --> < 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. 390 --> < p class = "noindent" > See  Note.< / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-7-4-5"
class="td11"><!-- l. 391 --> < 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 = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-7-5-1"
class="td11">< 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 >
< / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-6-">< td colspan = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-7-6-1"
class="td11">< 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 >
< / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-7-">< td colspan = "5" style = "white-space:nowrap; text-align:left;" id = "TBL-7-7-1"
class="td11">< 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 >
< / 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-7-8-">< 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. 415 --> < p class = "indent" > < a
id="x21-200136">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 415 --> < 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. 418 --> < 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. 418 --> < 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. 418 --> < 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. 419 --> < 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. 420 --> < 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. 421 --> < p class = "noindent" > Any integer
<!-- l. 421 --> < 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. 422 --> < p class = "noindent" > 10 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-8-2-5"
class="td11"><!-- l. 423 --> < 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. 425 --> < 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. 426 --> < p class = "noindent" > Any integer
<!-- l. 426 --> < 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. 427 --> < p class = "noindent" > 0 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-8-3-5"
class="td11"><!-- l. 428 --> < 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. 429 --> < 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. 431 --> < p class = "noindent" > Any real
<!-- l. 431 --> < 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. 432 --> < p class = "noindent" > 0 < / td > < td style = "white-space:wrap; text-align:left;" id = "TBL-8-4-5"
class="td11"><!-- l. 433 --> < 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. 442 --> < p class = "indent" > < a
id="x21-200147">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 442 --> < 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. 446 --> < 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. 446 --> < 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. 446 --> < 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. 447 --> < 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. 449 --> < 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. 450 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ JACOBI’ < / span > < / span > < / span >
<!-- l. 450 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ GS’ < / span > < / span > < / span >
<!-- l. 450 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ BGS’ < / span > < / span > < / span >
<!-- l. 450 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ BJAC’ < / span > < / span > < / span >
<!-- l. 451 --> < 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. 452 --> < 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. 453 --> < 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. 457 --> < 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. 458 --> < 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. 459 --> < p class = "noindent" > < span
class="cmtt-10">’ JACOBI’ < / span >
<!-- l. 460 --> < p class = "noindent" > < span
class="cmtt-10">’ GS’ < / span >
<!-- l. 460 --> < p class = "noindent" > < span
class="cmtt-10">’ BGS’ < / span >
<!-- l. 460 --> < p class = "noindent" > < span
class="cmtt-10">’ ILU’ < / span >
<!-- l. 461 --> < p class = "noindent" > < span
class="cmtt-10">’ ILUT’ < / span >
<!-- l. 461 --> < p class = "noindent" > < span
class="cmtt-10">’ MILU’ < / span >
<!-- l. 462 --> < p class = "noindent" > < span
class="cmtt-10">’ MUMPS’ < / span >
<!-- l. 462 --> < p class = "noindent" > < span
class="cmtt-10">’ SLU’ < / span >
<!-- l. 462 --> < 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. 463 --> < 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. 465 --> < 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. 467 --> < 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. 474 --> < 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. 475 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 475 --> < 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. 476 --> < 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. 477 --> < 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. 482 --> < 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. 483 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 483 --> < 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. 484 --> < 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. 485 --> < 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. 494 --> < p class = "indent" > < a
id="x21-200158">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 494 --> < 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. 498 --> < 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. 498 --> < 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. 498 --> < 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. 499 --> < 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. 500 --> < 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. 501 --> < p class = "noindent" > < span
class="cmtt-10">’ HALO’ < / span >
<!-- l. 501 --> < 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. 502 --> < 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. 503 --> < 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. 506 --> < 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. 508 --> < 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. 509 --> < p class = "noindent" > < span
class="cmtt-10">’ SUM’ < / span >
<!-- l. 509 --> < 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. 510 --> < 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. 511 --> < 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. 514 --> < 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. 516 --> < 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. 517 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 517 --> < 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. 518 --> < 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. 519 --> < 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. 520 --> < 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. 521 --> < 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. 522 --> < 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. 523 --> < 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. 524 --> < 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. 525 --> < p class = "noindent" > < span
class="cmtt-10">LOCAL< / span > < span
class="cmtt-10">_SOLVER’ < / span >
<!-- l. 525 --> < 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. 526 --> < 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. 527 --> < 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. 531 --> < 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. 532 --> < 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. 533 --> < 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. 534 --> < 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. 536 --> < 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. 537 --> < 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. 538 --> < 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. 539 --> < 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. 551 --> < 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. 551 --> < p class = "indent" > < a
id="tailuserhtmlsu11.html">< / a >
< / body > < / html >
