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pasquadambra
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This section describes the basics for building and applying
AMG4PSBLAS one-level and multilevel (i.e., AMG) preconditioners with
the Krylov solvers included in PSBLAS \cite{PSBLASGUIDE}.
the Krylov solvers included in PSBLAS~\cite{PSBLASGUIDE}.
The following steps are required:
\begin{enumerate}
@@ -108,7 +108,7 @@ usually lead to smaller numbers of preconditioned Krylov
iterations than inexact solvers, when the linear system comes from
a standard discretization of basic scalar elliptic PDE problems. However,
this does not necessarily correspond to the shortest execution time
on parallel computers.
on parallel~computers.
\subsection{Examples\label{sec:examples}}
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pdfpagelabels,
colorlinks,
citecolor=red,
linkcolor=blue]{hyperref}
linkcolor=blue,
pdfauthor={Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone},
pdftitle={Algebraic MultiGrid Preconditioners Package based on PSBLAS, V. 1.0},
pdfsubject={MultiGrid Parallel Preconditioners Package},
pdfkeywords={Parallel Numerical Software, Algebraic MultiGrid Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI},
]{hyperref}
\usepackage{html}
\usepackage{ifthen}
\usepackage{graphicx}
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@@ -14,7 +14,7 @@ For backward compatibility, methods are also accessible as
stand-alone subroutines.
For each method, the same user interface is overloaded with
respect to the real/complex and single/double precision data;
respect to the real/\-com\-plex and single/double precision data;
arguments with appropriate data types must be passed to the method, i.e.,
\begin{itemize}
\item the sparse matrix data structure, containing the matrix to be
@@ -282,11 +282,11 @@ be applied.
& Parallel aggregation algorithm. \par the
\fortinline|SYMDEC| option applies decoupled
aggregation to the sparsity pattern
of $A+A^T$.\\ \hline
of $A+A^T$.\\\hline%
\ifpdf
\phantomcaption
\end{tabular}
\end{center}
\phantomcaption
\esideways
\bsideways
\ContinuedFloat
@@ -414,11 +414,11 @@ the parameter \texttt{ilev}.} \\
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. \\ \hline
are available only in double precision. \\\hline%
\ifpdf
\phantomcaption
\end{tabular}
\end{center}
\phantomcaption
\esideways
\bsideways
\ContinuedFloat
@@ -498,9 +498,9 @@ level (continued).\label{tab:p_coarse_1}}
\textsc{comments} \\ \hline
\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
\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
\fortinline|'BJAC_ITRACE'| & \fortinline|integer| & Any integer $>0$ & -1 & Number of iterations after which a trace is to be printed. \\ \hline
\fortinline|'BJAC_RESCHECK'|& \fortinline|integer| & Any integer $>0$ & -1 & Number of iterations after which a residual is to be calculated. \\ \hline
\fortinline|'BJAC_STOPTOL'| & \fortinline|real(kind_parameter)| & Any real $<1$ & 0 & Tolerance for the stopping criterion on the residual. \\ \hline
\fortinline|'BJAC_ITRACE'| & \fortinline|integer| & Any integer\par $>0$ & -1 & Number of iterations after which a trace is to be printed. \\ \hline
\fortinline|'BJAC_RESCHECK'|& \fortinline|integer| & Any integer\par $>0$ & -1 & Number of iterations after which a residual is to be calculated. \\ \hline
\fortinline|'BJAC_STOPTOL'| & \fortinline|real(kind_parameter)| & Any real\par $<1$ & 0 & Tolerance for the stopping criterion on the residual. \\ \hline
\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
used. \texttt{CG} the Conjugate Gradient method;
\texttt{CGS} the Conjugate Gradient Stabilized method;
@@ -510,11 +510,11 @@ level (continued).\label{tab:p_coarse_1}}
\texttt{BICGSTAB} the Bi-Conjugate Gradient Stabilized method;
\texttt{BICGSTABL} the Bi-Conjugate Gradient Stabilized method with restarting;
\texttt{RGMRES} the Generalized Minimal Residual method with restarting. Refer to the PSBLAS guide~\cite{PSBLASGUIDE} for further information. \\ \hline
\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
\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%
\ifpdf
\phantomcaption
\end{tabular}
\end{center}
\phantomcaption
\esideways
\bsideways
\ContinuedFloat