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@@ -36,7 +36,8 @@ class="cmr-12">This section describes the basics for building and applying AMG4P
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<span
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class="cmr-12">and multilevel (i.e., AMG) preconditioners with the Krylov solvers included in</span>
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<span
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class="cmr-12">PSBLAS </span><span class="cite"><span
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class="cmr-12">PSBLAS</span><span
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class="cmr-12"> </span><span class="cite"><span
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class="cmr-12">[</span><a
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href="userhtmlli5.html#XPSBLASGUIDE"><span
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class="cmr-12">18</span></a><span
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@@ -432,7 +433,8 @@ class="cmr-12">linear system comes from a standard discretization of basic scala
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<span
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class="cmr-12">problems. However, this does not necessarily correspond to the shortest execution time</span>
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<span
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class="cmr-12">on parallel computers.</span>
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class="cmr-12">on parallel</span><span
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class="cmr-12"> computers.</span>
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<div class="subsectionTOCS">
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<span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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@@ -1565,7 +1565,7 @@ class="cmtt-10x-x-109">’</span> </td><td style="white-space:nowrap;
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class="td11"><span class="lstinline"></span><!--l. 501--><p class="noindent" ><span
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class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-3"
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class="td11"><!--l. 501--><p class="noindent" >Any integer
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<span
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<!--l. 501--><p class="noindent" ><span
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class="cmmi-10x-x-109">> </span>0 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-4"
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class="td11"><!--l. 501--><p class="noindent" >-1 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-4-5"
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class="td11"><!--l. 501--><p class="noindent" >Number of iterations after which a trace is to
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@@ -1580,7 +1580,7 @@ class="cmtt-10x-x-109">’</span> </td><td style="white-space:nowrap; t
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class="td11"><span class="lstinline"></span><!--l. 502--><p class="noindent" ><span
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class="cmtt-10x-x-109">integer</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-3"
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class="td11"><!--l. 502--><p class="noindent" >Any integer
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<span
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<!--l. 502--><p class="noindent" ><span
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class="cmmi-10x-x-109">> </span>0 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-4"
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class="td11"><!--l. 502--><p class="noindent" >-1 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-5-5"
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class="td11"><!--l. 502--><p class="noindent" >Number of iterations after which a residual is
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@@ -1597,9 +1597,9 @@ class="cmtt-10x-x-109">real</span><span
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class="cmtt-10x-x-109">(</span><span
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class="cmtt-10x-x-109">kind_parameter</span><span
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class="cmtt-10x-x-109">)</span> </td><td style="white-space:wrap; text-align:left;" id="TBL-8-6-3"
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class="td11"><!--l. 503--><p class="noindent" >Any real <span
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class="cmmi-10x-x-109"><</span>
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1 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-6-4"
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class="td11"><!--l. 503--><p class="noindent" >Any real
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<!--l. 503--><p class="noindent" ><span
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class="cmmi-10x-x-109">< </span>1 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-6-4"
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class="td11"><!--l. 503--><p class="noindent" >0 </td><td style="white-space:wrap; text-align:left;" id="TBL-8-6-5"
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class="td11"><!--l. 503--><p class="noindent" >Tolerance for the stopping criterion on the
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residual. </td>
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@@ -4,7 +4,7 @@
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This section describes the basics for building and applying
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AMG4PSBLAS one-level and multilevel (i.e., AMG) preconditioners with
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the Krylov solvers included in PSBLAS \cite{PSBLASGUIDE}.
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the Krylov solvers included in PSBLAS~\cite{PSBLASGUIDE}.
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The following steps are required:
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\begin{enumerate}
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@@ -108,7 +108,7 @@ usually lead to smaller numbers of preconditioned Krylov
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iterations than inexact solvers, when the linear system comes from
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a standard discretization of basic scalar elliptic PDE problems. However,
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this does not necessarily correspond to the shortest execution time
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on parallel computers.
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on parallel~computers.
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\subsection{Examples\label{sec:examples}}
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@@ -14,7 +14,7 @@ For backward compatibility, methods are also accessible as
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stand-alone subroutines.
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For each method, the same user interface is overloaded with
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respect to the real/complex and single/double precision data;
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respect to the real/\-com\-plex and single/double precision data;
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arguments with appropriate data types must be passed to the method, i.e.,
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\begin{itemize}
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\item the sparse matrix data structure, containing the matrix to be
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@@ -498,9 +498,9 @@ level (continued).\label{tab:p_coarse_1}}
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\textsc{comments} \\ \hline
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\fortinline|'BJAC_STOP'| & \fortinline|character(len=*)| & \fortinline|'FALSE'| \par \fortinline|'TRUE'| & \fortinline|'FALSE'| & Select whether to use a stopping criterion for the Block-Jacobi method used as a coarse solver. \\ \hline
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\fortinline|'BJAC_TRACE'| & \fortinline|character(len=*)| & \fortinline|'FALSE'| \par \fortinline|'TRUE'| & \fortinline|'FALSE'| & Select whether to print a trace for the calculated residual for the Block-Jacobi method used as a coarse solver. \\ \hline
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\fortinline|'BJAC_ITRACE'| & \fortinline|integer| & Any integer $>0$ & -1 & Number of iterations after which a trace is to be printed. \\ \hline
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\fortinline|'BJAC_RESCHECK'|& \fortinline|integer| & Any integer $>0$ & -1 & Number of iterations after which a residual is to be calculated. \\ \hline
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\fortinline|'BJAC_STOPTOL'| & \fortinline|real(kind_parameter)| & Any real $<1$ & 0 & Tolerance for the stopping criterion on the residual. \\ \hline
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\fortinline|'BJAC_ITRACE'| & \fortinline|integer| & Any integer\par $>0$ & -1 & Number of iterations after which a trace is to be printed. \\ \hline
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\fortinline|'BJAC_RESCHECK'|& \fortinline|integer| & Any integer\par $>0$ & -1 & Number of iterations after which a residual is to be calculated. \\ \hline
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\fortinline|'BJAC_STOPTOL'| & \fortinline|real(kind_parameter)| & Any real\par $<1$ & 0 & Tolerance for the stopping criterion on the residual. \\ \hline
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\fortinline|'KRM_METHOD'| & \fortinline|character(len=*)| & \fortinline|'CG'| \par \fortinline|'FCG'| \par \fortinline|'CGS'| \par \fortinline|'CGR'| \par \fortinline|'BICG'| \par \fortinline|'BICGSTAB'| \par \fortinline|'BICGSTABL'| \par \fortinline|'RGMRES'| & \fortinline|'FCG'| & A string that defines the iterative method to be
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used. \texttt{CG} the Conjugate Gradient method;
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\texttt{CGS} the Conjugate Gradient Stabilized method;
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@@ -510,7 +510,7 @@ level (continued).\label{tab:p_coarse_1}}
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\texttt{BICGSTAB} the Bi-Conjugate Gradient Stabilized method;
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\texttt{BICGSTABL} the Bi-Conjugate Gradient Stabilized method with restarting;
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\texttt{RGMRES} the Generalized Minimal Residual method with restarting. Refer to the PSBLAS guide~\cite{PSBLASGUIDE} for further information. \\ \hline
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\fortinline|'KRM_KPREC'| & \fortinline|character(len=*)| & Table~\ref{tab:precinit} & \fortinline|'BJAC'| & The one-level preconditioners from the Table~\ref{tab:precinit} can be used for the coarse Krylov solver. \\ \hline
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\fortinline|'KRM_KPREC'| & \fortinline|character(len=*)| & Table~\ref{tab:precinit} & \fortinline|'BJAC'| & The one-level preconditioners from the Table~\ref{tab:precinit} can be used for the coarse Krylov solver.\\ \hline
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\ifpdf
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\phantomcaption
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\end{tabular}
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