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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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-2-1"
class="td11"><!-- l. 88 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-4-1"
class="td11"><!-- l. 94 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-6-1"
class="td11"><!-- l. 100 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-8-1"
class="td11"><!-- l. 103 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-10-1"
class="td11"><!-- l. 111 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-12-1"
class="td11"><!-- l. 119 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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:normal; 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:normal; 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:normal; text-align:left;" id = "TBL-3-14-1"
class="td11"><!-- l. 125 --> < p class = "noindent" > < / td > < td style = "white-space:normal; 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 coarsening 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">.< / span > < br
class="newline" />
<!-- l. 150 --> < 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 point-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. 167 --> < 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. 176 --> < 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. 180 --> < 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. 185 --> < p class = "indent" > < span
class="cmr-12">More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be< / span >
< span
class="cmr-12">replicated, while SuperLU< / span > < span
class="cmr-12">_Dist 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. 200 --> < p class = "indent" > < span
class="cmr-12">On the other hand, the distributed layout can be used with any solver but< / span >
< span
class="cmr-12">UMFPACK and SuperLU; therefore, if any of these two solvers has already been< / span >
< span
class="cmr-12">selected, the coarsest-level solver is changed to block-Jacobi, with the previously< / 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. 208 --> < 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. 219 --> < p class = "indent" > < a
id="x21-200092">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 219 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-4" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-4-1g" > < col
id="TBL-4-1">< / colgroup > < colgroup id = "TBL-4-2g" > < col
id="TBL-4-2">< / colgroup > < colgroup id = "TBL-4-3g" > < col
id="TBL-4-3">< / colgroup > < colgroup id = "TBL-4-4g" > < col
id="TBL-4-4">< / colgroup > < colgroup id = "TBL-4-5g" > < col
id="TBL-4-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-4-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-4-1-1"
class="td11"><!-- l. 223 --> < 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:normal; text-align:left;" id = "TBL-4-1-3"
class="td11"><!-- l. 223 --> < 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:normal; text-align:left;" id = "TBL-4-1-4"
class="td11"><!-- l. 223 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-4-1-5"
class="td11"><!-- l. 224 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-4-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-4-2-1"
class="td11"><!-- l. 225 --> < 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:normal; text-align:left;" id = "TBL-4-2-3"
class="td11"><!-- l. 226 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ VCYCLE’ < / span >
<!-- l. 226 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ WCYCLE’ < / span >
<!-- l. 226 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ KCYCLE’ < / span >
<!-- l. 226 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ ADD’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-4-2-4"
class="td11"><!-- l. 227 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ VCYCLE’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-4-2-5"
class="td11"><!-- l. 228 --> < p class = "noindent" > Multilevel cycle: V-cycle, W-cycle, K-cycle,
and additive composition. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-4-3-">< td style = "white-space:normal; text-align:left;" id = "TBL-4-3-1"
class="td11"><!-- l. 229 --> < 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:normal; text-align:left;" id = "TBL-4-3-3"
class="td11"><!-- l. 230 --> < p class = "noindent" > Any integer
<!-- l. 230 --> < p class = "noindent" > number < span
class="cmsy-10x-x-109">≥ < / span > 1 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-4-3-4"
class="td11"><!-- l. 230 --> < p class = "noindent" > 1 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-4-3-5"
class="td11"><!-- l. 231 --> < p class = "noindent" > Number of multilevel cycles. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-4-4-">< td style = "white-space:normal; text-align:left;" id = "TBL-4-4-1"
class="td11"> < / td > < / tr > < / table > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Table  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. 241 --> < p class = "indent" > < a
id="x21-200103">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 241 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-5" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-5-1g" > < col
id="TBL-5-1">< / colgroup > < colgroup id = "TBL-5-2g" > < col
id="TBL-5-2">< / colgroup > < colgroup id = "TBL-5-3g" > < col
id="TBL-5-3">< / colgroup > < colgroup id = "TBL-5-4g" > < col
id="TBL-5-4">< / colgroup > < colgroup id = "TBL-5-5g" > < col
id="TBL-5-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-1-1"
class="td11"><!-- l. 245 --> < 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:normal; text-align:left;" id = "TBL-5-1-3"
class="td11"><!-- l. 245 --> < 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:normal; text-align:left;" id = "TBL-5-1-4"
class="td11"><!-- l. 245 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-1-5"
class="td11"><!-- l. 246 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-2-1"
class="td11"><!-- l. 247 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">’ MIN_COARSE_SIZE_PER_PROCESS’ < / 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:normal; text-align:left;" id = "TBL-5-2-3"
class="td11"><!-- l. 248 --> < p class = "noindent" > Any number
<!-- l. 248 --> < p class = "noindent" > < span
class="cmmi-10x-x-109">> < / span > 0 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-2-4"
class="td11"><!-- l. 249 --> < p class = "noindent" > 200 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-2-5"
class="td11"><!-- l. 250 --> < p class = "noindent" > Coarse size threshold per process. The
aggregation stops if the global number of
variables of the computed coarsest matrix
is lower than or equal to this threshold
multiplied by the number of processes.
<!-- l. 256 --> < 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:normal; text-align:left;" id = "TBL-5-3-1"
class="td11"><!-- l. 257 --> < 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-5-3-2"
class="td11">< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">integer< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-3-3"
class="td11"><!-- l. 258 --> < p class = "noindent" > Any number
<!-- l. 258 --> < p class = "noindent" > < span
class="cmmi-10x-x-109">> < / span > 0 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-3-4"
class="td11"><!-- l. 259 --> < p class = "noindent" > -1 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-3-5"
class="td11"><!-- l. 260 --> < p class = "noindent" > Coarse size threshold. The aggregation
stops if the global number of variables
of the computed coarsest matrix is lower
than or equal
to this threshold (see Note). If negative,
it is ignored in favour of the default for
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">’ MIN_COARSE_SIZE_PER_PROCESS’ < / span > < / 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-5-4-">< td style = "white-space:normal; 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">’ MIN_CR_RATIO’ < / 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">real< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-4-3"
class="td11"><!-- l. 270 --> < p class = "noindent" > Any number
<!-- l. 270 --> < p class = "noindent" > < span
class="cmmi-10x-x-109">> < / span > 1 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-4-4"
class="td11"><!-- l. 271 --> < p class = "noindent" > 1.5 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-4-5"
class="td11"><!-- l. 272 --> < p class = "noindent" > Minimum coarsening
ratio. The aggregation stops if the ratio
between the global matrix dimensions at
two consecutive levels is lower than or
equal to this threshold (see Note). < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-5-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-5-1"
class="td11"><!-- l. 277 --> < 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-5-5-2"
class="td11">< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">integer< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-5-3"
class="td11"><!-- l. 278 --> < p class = "noindent" > Any integer
<!-- l. 278 --> < p class = "noindent" > number < span
class="cmmi-10x-x-109">> < / span > 1 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-5-4"
class="td11"><!-- l. 279 --> < p class = "noindent" > 20 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-5-5"
class="td11"><!-- l. 280 --> < p class = "noindent" > Maximum number of levels. The
aggregation stops if the number of levels
reaches this value (see Note). < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-6-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-6-1"
class="td11"><!-- l. 283 --> < 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-5-6-2"
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:normal; text-align:left;" id = "TBL-5-6-3"
class="td11"><!-- l. 284 --> < 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:normal; text-align:left;" id = "TBL-5-6-4"
class="td11"><!-- l. 285 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ DEC’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-6-5"
class="td11"><!-- l. 286 --> < p class = "noindent" > Parallel aggregation algorithm.
<!-- l. 286 --> < p class = "noindent" > 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-5-7-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-7-1"
class="td11"><!-- l. 291 --> < 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-5-7-2"
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:normal; text-align:left;" id = "TBL-5-7-3"
class="td11"><!-- l. 292 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SOC1’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-7-4"
class="td11"><!-- l. 293 --> < 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:normal; text-align:left;" id = "TBL-5-7-5"
class="td11"><!-- l. 296 --> < p class = "noindent" > Type of aggregation algorithm: currently,
for the
decoupled aggregation we implement two
measures of strength of connection, the
one by Vaně k, Mandel and Brezina  < span class = "cite" > [< a
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">29< / a > ]< / span > ,
and the one by Gratton et al  < span class = "cite" > [< a
href="userhtmlli4.html#XGrHeJi:16">19< / a > ]< / span > . The
coupled aggregation is based on a parallel
version of the half-approximate matching
implemented in the MatchBox-P software
package < span
class="cmbx-10x-x-109">AGGIUNGERE LINK AL< / span >
< span
class="cmbx-10x-x-109">PACKAGE?< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-8-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-8-1"
class="td11"><!-- l. 305 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">’ AGGR_SIZE’ < / span > < / span > < / span > < / td > < td style = "white-space:nowrap; text-align:left;" id = "TBL-5-8-2"
class="td11">< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10x-x-109">integer< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-8-3"
class="td11"><!-- l. 306 --> < p class = "noindent" > Any integer
<!-- l. 306 --> < p class = "noindent" > number
power of 2
and < span
class="cmmi-10x-x-109">> < / span > 2 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-8-4"
class="td11"><!-- l. 307 --> < p class = "noindent" > 4 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-8-5"
class="td11"><!-- l. 308 --> < p class = "noindent" > Maximum size of aggregates when the
coupled aggregation based on matching
is applied. For aggressive coarsening
with size of aggregate larger than 8
we recommend the use of smoothed
prolongators. < span
class="cmbx-10x-x-109">MODIFICARE< / span >
< span
class="cmbx-10x-x-109">CODICE< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-9-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-9-1"
class="td11"><!-- l. 313 --> < 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-5-9-2"
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:normal; text-align:left;" id = "TBL-5-9-3"
class="td11"><!-- l. 314 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SMOOTHED’ < / span > ,
< span
class="cmtt-10x-x-109">’ UNSMOOTHED’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-9-4"
class="td11"><!-- l. 314 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SMOOTHED’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-5-9-5"
class="td11"><!-- l. 315 --> < p class = "noindent" > Prolongator used by the aggregation
algorithm: smoothed or unsmoothed (i.e.,
tentative prolongator). < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-10-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-5-10-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > < span
class="cmbx-10x-x-109">Note. < / span > The aggregation algorithm stops when at least one of the following criteria is met: the coarse size threshold, the coarse size threshold per process, the< / div >
< / tr > < tr
style="vertical-align:baseline;" id="TBL-5-11-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-5-11-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > minimum coarsening ratio, or the maximum number of levels is reached. Therefore, the actual number of levels may be< / div >
< / tr > < tr
style="vertical-align:baseline;" id="TBL-5-12-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-5-12-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > smaller than the specified maximum number of levels. < / div >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-5-13-">< td style = "white-space:normal; text-align:left;" id = "TBL-5-13-1"
class="td11"> < / td > < / tr > < / table >
< / div > < / 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. 333 --> < p class = "indent" > < a
id="x21-200114">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 333 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-6" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-6-1g" > < col
id="TBL-6-1">< / colgroup > < colgroup id = "TBL-6-2g" > < col
id="TBL-6-2">< / colgroup > < colgroup id = "TBL-6-3g" > < col
id="TBL-6-3">< / colgroup > < colgroup id = "TBL-6-4g" > < col
id="TBL-6-4">< / colgroup > < colgroup id = "TBL-6-5g" > < col
id="TBL-6-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-6-1-1"
class="td11"><!-- l. 337 --> < 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:normal; text-align:left;" id = "TBL-6-1-3"
class="td11"><!-- l. 337 --> < 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:normal; text-align:left;" id = "TBL-6-1-4"
class="td11"><!-- l. 337 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-1-5"
class="td11"><!-- l. 338 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-6-2-1"
class="td11"><!-- l. 340 --> < 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:normal; text-align:left;" id = "TBL-6-2-3"
class="td11"><!-- l. 341 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ NATURAL’ < / span >
<!-- l. 341 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ DEGREE’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-2-4"
class="td11"><!-- l. 342 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ NATURAL’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-2-5"
class="td11"><!-- l. 343 --> < p class = "noindent" > Initial ordering of indices for
the decoupled aggregation algorithm:
either natural ordering or sorted by
descending degrees of the nodes in the
matrix graph. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-3-">< td style = "white-space:normal; text-align:left;" id = "TBL-6-3-1"
class="td11"><!-- l. 350 --> < 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:normal; text-align:left;" id = "TBL-6-3-3"
class="td11"><!-- l. 351 --> < p class = "noindent" > Any  real
<!-- l. 351 --> < 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:normal; text-align:left;" id = "TBL-6-3-4"
class="td11"><!-- l. 352 --> < p class = "noindent" > 0.01 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-3-5"
class="td11"><!-- l. 353 --> < p class = "noindent" > The threshold < span
class="cmmi-10x-x-109">θ < / span > in the decoupled
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:normal; text-align:left;" id = "TBL-6-4-1"
class="td11"><!-- l. 356 --> < 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:normal; text-align:left;" id = "TBL-6-4-3"
class="td11"><!-- l. 358 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ FILTER’ < / span >
<!-- l. 358 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ NOFILTER’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-4-4"
class="td11"><!-- l. 359 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ NOFILTER’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-6-4-5"
class="td11"><!-- l. 359 --> < p class = "noindent" > Matrix used in computing the smoothed
prolongator: filtered or unfiltered
(see  (< a
href="userhtmlsu7.html#x15-14009r5">5<!-- tex4ht:ref: eq:filtered --> < / a > ) in Section  < a
href="userhtmlsu7.html#x15-140004.2">4.2<!-- tex4ht:ref: sec:aggregation --> < / a > ). < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-5-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-6-5-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > < span
class="cmbx-10x-x-109">Note. < / span > Different thresholds at different levels, such as those used in < span class = "cite" > [< a
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">29< / a > , Section  5.1]< / span > , can be easily set by invoking the rou-< / div >
< / tr > < tr
style="vertical-align:baseline;" id="TBL-6-6-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-6-6-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > tine < span
class="cmtt-10x-x-109">set < / span > with the parameter < span
class="cmtt-10x-x-109">ilev< / span > .< / div >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-6-7-">< td style = "white-space:normal; text-align:left;" id = "TBL-6-7-1"
class="td11"> < / td > < / tr > < / table > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Table  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. 375 --> < p class = "indent" > < a
id="x21-200125">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 375 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-7" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-7-1g" > < col
id="TBL-7-1">< / colgroup > < colgroup id = "TBL-7-2g" > < col
id="TBL-7-2">< / colgroup > < colgroup id = "TBL-7-3g" > < col
id="TBL-7-3">< / colgroup > < colgroup id = "TBL-7-4g" > < col
id="TBL-7-4">< / colgroup > < colgroup id = "TBL-7-5g" > < col
id="TBL-7-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-7-1-1"
class="td11"><!-- l. 378 --> < 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:normal; text-align:left;" id = "TBL-7-1-3"
class="td11"><!-- l. 378 --> < 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:normal; text-align:left;" id = "TBL-7-1-4"
class="td11"><!-- l. 378 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-1-5"
class="td11"><!-- l. 379 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-7-2-1"
class="td11"><!-- l. 380 --> < 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:normal; text-align:left;" id = "TBL-7-2-3"
class="td11"><!-- l. 381 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ DIST’ < / span >
<!-- l. 381 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ REPL’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-2-4"
class="td11"><!-- l. 382 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ REPL’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-2-5"
class="td11"><!-- l. 383 --> < p class = "noindent" > Coarsest matrix layout: distributed among the
processes or replicated on each of them. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-3-">< td style = "white-space:normal; text-align:left;" id = "TBL-7-3-1"
class="td11"><!-- l. 385 --> < 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:normal; text-align:left;" id = "TBL-7-3-3"
class="td11"><!-- l. 386 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MUMPS’ < / span >
<!-- l. 386 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ UMF’ < / span >
<!-- l. 387 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLU’ < / span >
<!-- l. 387 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLUDIST’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ JACOBI’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ GS’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ BJAC’ < / span >
<!-- l. 388 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ PCG’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-3-4"
class="td11"><!-- l. 389 --> < p class = "noindent" > See  Note.< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-3-5"
class="td11"><!-- l. 390 --> < p class = "noindent" > Solver used at the coarsest level: sequential LU
from MUMPS, UMFPACK, or SuperLU (plus
triangular solve); distributed LU from MUMPS or
SuperLU_Dist (plus triangular solve); point-Jacobi,
hybrid Gauss-Seidel or block-Jacobi and related
< span
class="cmmi-10x-x-109">ℓ < / span > < sub > < span
class="cmr-8">1< / span > < / sub > -versions;
< span
class="cmbx-10x-x-109">preconditioned Conjugate Gradient coupled< / span >
< span
class="cmbx-10x-x-109">with the block-Jacobi preconditioner with< / span >
< span
class="cmbx-10x-x-109">ILU(0) on the blocks< / span > .
<!-- l. 398 --> < 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 > , < span
class="cmtt-10x-x-109">BJAC < / span > and < span
class="cmtt-10x-x-109">PCG< / span >
require it to be distributed, < span
class="cmtt-10x-x-109">MUMPS < / span > can be used with
either a replicated or a distributed matrix. When
any of the previous solvers is specified, the matrix
layout is set to a default value which allows the use
of the solver (see Remark 3, p.  24). Note also that
UMFPACK and SuperLU_Dist are available only in
double precision. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-4-">< td style = "white-space:normal; text-align:left;" id = "TBL-7-4-1"
class="td11"><!-- l. 407 --> < 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:normal; text-align:left;" id = "TBL-7-4-3"
class="td11"><!-- l. 408 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ ILU’ < / span >
<!-- l. 408 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ ILUT’ < / span >
<!-- l. 408 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MILU’ < / span >
<!-- l. 409 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ MUMPS’ < / span >
<!-- l. 409 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ SLU’ < / span >
<!-- l. 409 --> < p class = "noindent" > < span
class="cmtt-10x-x-109">’ UMF’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-4-4"
class="td11"><!-- l. 410 --> < p class = "noindent" > See  Note.< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-7-4-5"
class="td11"><!-- l. 411 --> < 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). < span
class="cmbx-10x-x-109">Aggiungere Sparse< / span >
< span
class="cmbx-10x-x-109">Approssimate per GPU? < / span > Note that UMFPACK
and SuperLU_Dist are available only in double
precision. < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-5-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-7-5-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > < span
class="cmbx-10x-x-109">Note. < / span > Defaults for < span
class="cmtt-10x-x-109">COARSE< / span > < span
class="cmtt-10x-x-109">_SOLVE < / span > and < span
class="cmtt-10x-x-109">COARSE< / span > < span
class="cmtt-10x-x-109">_SUBSOLVE < / span > are chosen in the following order:< / div >
< / tr > < tr
style="vertical-align:baseline;" id="TBL-7-6-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-7-6-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > single precision version – < span
class="cmtt-10x-x-109">MUMPS < / span > if installed, then < span
class="cmtt-10x-x-109">SLU < / span > if installed, < span
class="cmtt-10x-x-109">ILU < / span > otherwise;< / div >
< / tr > < tr
style="vertical-align:baseline;" id="TBL-7-7-">< td colspan = "3" style = "white-space:normal; text-align:left;" id = "TBL-7-7-1"
class="td11">< / td > < div class = "multicolumn" style = "white-space:nowrap; text-align:left;" > double precision version – < span
class="cmtt-10x-x-109">UMF < / span > if installed, then < span
class="cmtt-10x-x-109">MUMPS < / span > if installed, then < span
class="cmtt-10x-x-109">SLU < / span > if installed, < span
class="cmtt-10x-x-109">ILU < / span > otherwise.< / div >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-7-8-">< td style = "white-space:normal; text-align:left;" id = "TBL-7-8-1"
class="td11"> < / 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. 435 --> < p class = "indent" > < a
id="x21-200136">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 435 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-8" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-8-1g" > < col
id="TBL-8-1">< / colgroup > < colgroup id = "TBL-8-2g" > < col
id="TBL-8-2">< / colgroup > < colgroup id = "TBL-8-3g" > < col
id="TBL-8-3">< / colgroup > < colgroup id = "TBL-8-4g" > < col
id="TBL-8-4">< / colgroup > < colgroup id = "TBL-8-5g" > < col
id="TBL-8-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-8-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-8-1-1"
class="td11"><!-- l. 438 --> < 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:normal; text-align:left;" id = "TBL-8-1-3"
class="td11"><!-- l. 438 --> < 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:normal; text-align:left;" id = "TBL-8-1-4"
class="td11"><!-- l. 438 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-1-5"
class="td11"><!-- l. 439 --> < p class = "noindent" > < span
class="cmcsc-10x-x-109">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-8-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-8-2-1"
class="td11"><!-- l. 440 --> < 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:normal; text-align:left;" id = "TBL-8-2-3"
class="td11"><!-- l. 441 --> < p class = "noindent" > Any integer
<!-- l. 441 --> < p class = "noindent" > number < span
class="cmmi-10x-x-109">> < / span > 0< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-2-4"
class="td11"><!-- l. 442 --> < p class = "noindent" > 10 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-2-5"
class="td11"><!-- l. 443 --> < 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. < span
class="cmbx-10x-x-109">Aggiungere< / span >
< span
class="cmbx-10x-x-109">criterio di arresto del PCG?< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-8-3-">< td style = "white-space:normal; text-align:left;" id = "TBL-8-3-1"
class="td11"><!-- l. 445 --> < 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:normal; text-align:left;" id = "TBL-8-3-3"
class="td11"><!-- l. 446 --> < p class = "noindent" > Any integer
<!-- l. 446 --> < p class = "noindent" > number < span
class="cmsy-10x-x-109">≥ < / span > 0< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-3-4"
class="td11"><!-- l. 447 --> < p class = "noindent" > 0 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-3-5"
class="td11"><!-- l. 448 --> < 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:normal; text-align:left;" id = "TBL-8-4-1"
class="td11"><!-- l. 449 --> < 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:normal; text-align:left;" id = "TBL-8-4-3"
class="td11"><!-- l. 451 --> < p class = "noindent" > Any real
<!-- l. 451 --> < p class = "noindent" > number < span
class="cmsy-10x-x-109">≥ < / span > 0< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-4-4"
class="td11"><!-- l. 452 --> < p class = "noindent" > 0 < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-8-4-5"
class="td11"><!-- l. 453 --> < 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:normal; 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. 462 --> < p class = "indent" > < a
id="x21-200147">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 462 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-9" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-9-1g" > < col
id="TBL-9-1">< / colgroup > < colgroup id = "TBL-9-2g" > < col
id="TBL-9-2">< / colgroup > < colgroup id = "TBL-9-3g" > < col
id="TBL-9-3">< / colgroup > < colgroup id = "TBL-9-4g" > < col
id="TBL-9-4">< / colgroup > < colgroup id = "TBL-9-5g" > < col
id="TBL-9-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-9-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-9-1-1"
class="td11"><!-- l. 466 --> < 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:normal; text-align:left;" id = "TBL-9-1-3"
class="td11"><!-- l. 466 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">val< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-1-4"
class="td11"><!-- l. 466 --> < p class = "noindent" > < span
class="cmcsc-10">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-1-5"
class="td11"><!-- l. 467 --> < p class = "noindent" > < span
class="cmcsc-10">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-9-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-9-2-1"
class="td11"><!-- l. 469 --> < 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:normal; text-align:left;" id = "TBL-9-2-3"
class="td11"><!-- l. 470 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ JACOBI’ < / span > < / span > < / span >
<!-- l. 470 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ GS’ < / span > < / span > < / span >
<!-- l. 470 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ BGS’ < / span > < / span > < / span >
<!-- l. 470 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ BJAC’ < / span > < / span > < / span >
<!-- l. 471 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ AS’ < / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-2-4"
class="td11"><!-- l. 472 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">’ FBGS’ < / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-2-5"
class="td11"><!-- l. 473 --> < p class = "noindent" > < span
class="cmr-10">Type of smoother used in the multilevel< / span >
< span
class="cmr-10">preconditioner: point-Jacobi, hybrid< / span >
< span
class="cmr-10">(forward) Gauss-Seidel, hybrid backward< / span >
< span
class="cmr-10">Gauss-Seidel, block-Jacobi, < / span > < span
class="cmmi-10">ℓ < / span > < sub > < span
class="cmr-7">1< / span > < / sub > < span
class="cmbx-10">-versions?< / span >
< span
class="cmr-10">and Additive Schwarz.< / span >
<!-- l. 477 --> < p class = "noindent" > < span
class="cmr-10">It is ignored by one-level preconditioners.< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-9-3-">< td style = "white-space:normal; text-align:left;" id = "TBL-9-3-1"
class="td11"><!-- l. 478 --> < 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:normal; text-align:left;" id = "TBL-9-3-3"
class="td11"><!-- l. 479 --> < p class = "noindent" > < span
class="cmtt-10">’ JACOBI’ < / span >
<!-- l. 480 --> < p class = "noindent" > < span
class="cmtt-10">’ GS’ < / span >
<!-- l. 480 --> < p class = "noindent" > < span
class="cmtt-10">’ BGS’ < / span >
<!-- l. 480 --> < p class = "noindent" > < span
class="cmtt-10">’ ILU’ < / span >
<!-- l. 481 --> < p class = "noindent" > < span
class="cmtt-10">’ ILUT’ < / span >
<!-- l. 481 --> < p class = "noindent" > < span
class="cmtt-10">’ MILU’ < / span >
<!-- l. 482 --> < p class = "noindent" > < span
class="cmtt-10">’ MUMPS’ < / span >
<!-- l. 482 --> < p class = "noindent" > < span
class="cmtt-10">’ SLU’ < / span >
<!-- l. 482 --> < p class = "noindent" > < span
class="cmtt-10">’ UMF’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-3-4"
class="td11"><!-- l. 483 --> < 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. 485 --> < 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 >
< span
class="cmmi-10">ℓ < / span > < sub > < span
class="cmr-7">1< / span > < / sub > < span
class="cmbx-10">-versions?< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-3-5"
class="td11"><!-- l. 488 --> < 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:normal; text-align:left;" id = "TBL-9-4-1"
class="td11"><!-- l. 495 --> < 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:normal; text-align:left;" id = "TBL-9-4-3"
class="td11"><!-- l. 496 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 496 --> < 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:normal; text-align:left;" id = "TBL-9-4-4"
class="td11"><!-- l. 497 --> < p class = "noindent" > < span
class="cmr-10">1< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-4-5"
class="td11"><!-- l. 498 --> < 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:normal; text-align:left;" id = "TBL-9-5-1"
class="td11"><!-- l. 503 --> < 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:normal; text-align:left;" id = "TBL-9-5-3"
class="td11"><!-- l. 504 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 504 --> < 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:normal; text-align:left;" id = "TBL-9-5-4"
class="td11"><!-- l. 505 --> < p class = "noindent" > < span
class="cmr-10">1< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-9-5-5"
class="td11"><!-- l. 506 --> < p class = "noindent" > < span
class="cmr-10">Number of overlap layers, for Additive< / span >
< span
class="cmr-10">Schwarz only.< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-9-6-">< td style = "white-space:normal; text-align:left;" id = "TBL-9-6-1"
class="td11"> < / td > < / tr > < / table > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Table  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. 515 --> < p class = "indent" > < a
id="x21-200158">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 515 --> < p class = "noindent" >
< div class = "tabular" > < table id = "TBL-10" class = "tabular"
cellspacing="0" cellpadding="0"
>< colgroup id = "TBL-10-1g" > < col
id="TBL-10-1">< / colgroup > < colgroup id = "TBL-10-2g" > < col
id="TBL-10-2">< / colgroup > < colgroup id = "TBL-10-3g" > < col
id="TBL-10-3">< / colgroup > < colgroup id = "TBL-10-4g" > < col
id="TBL-10-4">< / colgroup > < colgroup id = "TBL-10-5g" > < col
id="TBL-10-5">< / colgroup > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-10-1-">< td style = "white-space:normal; text-align:left;" id = "TBL-10-1-1"
class="td11"><!-- l. 519 --> < 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:normal; text-align:left;" id = "TBL-10-1-3"
class="td11"><!-- l. 519 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">val< / span > < / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-1-4"
class="td11"><!-- l. 519 --> < p class = "noindent" > < span
class="cmcsc-10">< span
class="small-caps">d< / span > < span
class="small-caps">e< / span > < span
class="small-caps">f< / span > < span
class="small-caps">a< / span > < span
class="small-caps">u< / span > < span
class="small-caps">l< / span > < span
class="small-caps">t< / span > < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-1-5"
class="td11"><!-- l. 520 --> < p class = "noindent" > < span
class="cmcsc-10">< span
class="small-caps">c< / span > < span
class="small-caps">o< / span > < span
class="small-caps">m< / span > < span
class="small-caps">m< / span > < span
class="small-caps">e< / span > < span
class="small-caps">n< / span > < span
class="small-caps">t< / span > < span
class="small-caps">s< / span > < / span > < / td > < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-10-2-">< td style = "white-space:normal; text-align:left;" id = "TBL-10-2-1"
class="td11"><!-- l. 521 --> < 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:normal; text-align:left;" id = "TBL-10-2-3"
class="td11"><!-- l. 522 --> < p class = "noindent" > < span
class="cmtt-10">’ HALO’ < / span >
<!-- l. 522 --> < p class = "noindent" > < span
class="cmtt-10">’ NONE’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-2-4"
class="td11"><!-- l. 523 --> < p class = "noindent" > < span
class="cmtt-10">’ HALO’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-2-5"
class="td11"><!-- l. 524 --> < 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. 527 --> < 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:normal; text-align:left;" id = "TBL-10-3-1"
class="td11"><!-- l. 529 --> < 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:normal; text-align:left;" id = "TBL-10-3-3"
class="td11"><!-- l. 530 --> < p class = "noindent" > < span
class="cmtt-10">’ SUM’ < / span >
<!-- l. 530 --> < p class = "noindent" > < span
class="cmtt-10">’ NONE’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-3-4"
class="td11"><!-- l. 531 --> < p class = "noindent" > < span
class="cmtt-10">’ NONE’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-3-5"
class="td11"><!-- l. 532 --> < 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. 535 --> < 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:normal; text-align:left;" id = "TBL-10-4-1"
class="td11"><!-- l. 537 --> < 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:normal; text-align:left;" id = "TBL-10-4-3"
class="td11"><!-- l. 538 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
<!-- l. 538 --> < 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:normal; text-align:left;" id = "TBL-10-4-4"
class="td11"><!-- l. 539 --> < p class = "noindent" > < span
class="cmr-10">0< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-4-5"
class="td11"><!-- l. 540 --> < p class = "noindent" > < span
class="cmr-10">Fill-in level < / span > < span
class="cmmi-10">p < / span > < span
class="cmr-10">of the incomplete LU< / span >
< span
class="cmr-10">factorizations.< / span > < / td >
< / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / td > < / tr > < tr
style="vertical-align:baseline;" id="TBL-10-5-">< td style = "white-space:normal; text-align:left;" id = "TBL-10-5-1"
class="td11"><!-- l. 541 --> < 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:normal; text-align:left;" id = "TBL-10-5-3"
class="td11"><!-- l. 542 --> < 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:normal; text-align:left;" id = "TBL-10-5-4"
class="td11"><!-- l. 543 --> < p class = "noindent" > < span
class="cmr-10">0< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-5-5"
class="td11"><!-- l. 544 --> < 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:normal; text-align:left;" id = "TBL-10-6-1"
class="td11"><!-- l. 545 --> < 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:normal; text-align:left;" id = "TBL-10-6-3"
class="td11"><!-- l. 546 --> < p class = "noindent" > < span
class="cmtt-10">LOCAL< / span > < span
class="cmtt-10">_SOLVER’ < / span >
<!-- l. 546 --> < p class = "noindent" > < span
class="cmtt-10">GLOBAL< / span > < span
class="cmtt-10">_SOLVER’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-6-4"
class="td11"><!-- l. 547 --> < p class = "noindent" > < span
class="cmtt-10">GLOBAL< / span > < span
class="cmtt-10">_SOLVER’ < / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-6-5"
class="td11"><!-- l. 548 --> < 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:normal; text-align:left;" id = "TBL-10-7-1"
class="td11"><!-- l. 552 --> < 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:normal; text-align:left;" id = "TBL-10-7-3"
class="td11"><!-- l. 553 --> < p class = "noindent" > < span
class="cmr-10">Any integer< / span >
< span
class="cmr-10">number< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-7-4"
class="td11"><!-- l. 554 --> < p class = "noindent" > < span
class="cmr-10">0< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-7-5"
class="td11"><!-- l. 555 --> < 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:normal; text-align:left;" id = "TBL-10-8-1"
class="td11"><!-- l. 557 --> < 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:normal; text-align:left;" id = "TBL-10-8-3"
class="td11"><!-- l. 558 --> < p class = "noindent" > < span
class="cmr-10">Any real< / span >
< span
class="cmr-10">number< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-8-4"
class="td11"><!-- l. 559 --> < p class = "noindent" > < span
class="cmr-10">0< / span > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-10-8-5"
class="td11"><!-- l. 560 --> < 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:normal; 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. 572 --> < 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. 572 --> < p class = "indent" > < a
id="tailuserhtmlsu11.html">< / a >
< / body > < / html >
