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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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@@ -12,7 +12,12 @@
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pdfpagelabels,
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colorlinks,
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citecolor=red,
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linkcolor=blue]{hyperref}
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linkcolor=blue,
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pdfauthor={Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone},
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pdftitle={Algebraic MultiGrid Preconditioners Package based on PSBLAS, V. 1.0},
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pdfsubject={MultiGrid Parallel Preconditioners Package},
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pdfkeywords={Parallel Numerical Software, Algebraic MultiGrid Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI},
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]{hyperref}
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\usepackage{html}
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\usepackage{ifthen}
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\usepackage{graphicx}
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+10
-10
@@ -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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@@ -282,11 +282,11 @@ be applied.
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& Parallel aggregation algorithm. \par the
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\fortinline|SYMDEC| option applies decoupled
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aggregation to the sparsity pattern
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of $A+A^T$.\\ \hline
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of $A+A^T$.\\\hline%
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\ifpdf
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\phantomcaption
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\end{tabular}
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\end{center}
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\phantomcaption
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\esideways
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\bsideways
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\ContinuedFloat
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@@ -414,11 +414,11 @@ the parameter \texttt{ilev}.} \\
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solvers is specified, the matrix layout is set to a default
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value which allows the use of the solver (see Remark 3, p.~24).
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Note also that UMFPACK and SuperLU\_Dist
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are available only in double precision. \\ \hline
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are available only in double precision. \\\hline%
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\ifpdf
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\phantomcaption
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\end{tabular}
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\end{center}
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\phantomcaption
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\esideways
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\bsideways
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\ContinuedFloat
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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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@@ -510,11 +510,11 @@ 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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\end{center}
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\phantomcaption
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\esideways
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\bsideways
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\ContinuedFloat
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