|
|
|
|
@ -6,7 +6,7 @@ The basic user interface of MLD2P4 consists of eight routines. The six
|
|
|
|
|
routines \verb|init|, \verb|set|,
|
|
|
|
|
\verb|hierarchy_build|, \verb|smoothers_build|,
|
|
|
|
|
\verb|bld|, and \verb|apply| encapsulate all the
|
|
|
|
|
functionalities for the setup and the application of any multi-level and one-level
|
|
|
|
|
functionalities for the setup and the application of any multilevel and one-level
|
|
|
|
|
preconditioner implemented in the package.
|
|
|
|
|
The routine \verb|free| deallocates the preconditioner data structure, while
|
|
|
|
|
\verb|descr| prints a description of the preconditioner setup by the user.
|
|
|
|
|
@ -63,7 +63,7 @@ This routine allocates and initializes the preconditioner
|
|
|
|
|
\verb|info| & \verb|integer, intent(out)|.\\
|
|
|
|
|
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
|
|
|
|
|
%\verb|nlev| & \verb|integer, optional, intent(in)|.\\
|
|
|
|
|
% & The number of levels of the multi-level
|
|
|
|
|
% & The number of levels of the multilevel
|
|
|
|
|
% preconditioner. This optional argument is deprecated,
|
|
|
|
|
% new codes should set the number of levels with \verb|mld_precset|.\\
|
|
|
|
|
% If \verb|nlev| is not present and \verb|ptype|=\verb|'ML'|, \verb|'ml'|,
|
|
|
|
|
@ -115,7 +115,7 @@ contained in \verb|val|.
|
|
|
|
|
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors}
|
|
|
|
|
for details.\\
|
|
|
|
|
\verb|ilev| & \verb|integer, optional, intent(in)|.\\
|
|
|
|
|
& For the multi-level preconditioner, the level at which the
|
|
|
|
|
& For the multilevel preconditioner, the level at which the
|
|
|
|
|
preconditioner parameter has to be set.
|
|
|
|
|
The levels are numbered in increasing
|
|
|
|
|
order starting from the finest one, i.e., level 1 is the finest level.
|
|
|
|
|
@ -123,7 +123,7 @@ contained in \verb|val|.
|
|
|
|
|
is set at all the appropriate levels (see
|
|
|
|
|
Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}).\\
|
|
|
|
|
\verb|ilmax| & \verb|integer, optional, intent(in)|.\\
|
|
|
|
|
& For the multi-level preconditioner, when both
|
|
|
|
|
& For the multilevel preconditioner, when both
|
|
|
|
|
\verb|ilev| and \verb|ilmax| are present, the settings
|
|
|
|
|
are applied at all levels \verb|ilev:ilmax|. When
|
|
|
|
|
\verb|ilev| is present but \verb|ilmax| is not, then
|
|
|
|
|
@ -154,11 +154,11 @@ A variety of preconditioners can be obtained
|
|
|
|
|
by a suitable setting of the preconditioner parameters. These parameters
|
|
|
|
|
can be logically divided into four groups, i.e., parameters defining
|
|
|
|
|
\begin{enumerate}
|
|
|
|
|
\item the type of multi-level cycle and how many cycles must be applied;
|
|
|
|
|
\item the type of multilevel cycle and how many cycles must be applied;
|
|
|
|
|
\item the aggregation algorithm;
|
|
|
|
|
\item the coarse-space correction at the coarsest level (for multi-level
|
|
|
|
|
\item the coarse-space correction at the coarsest level (for multilevel
|
|
|
|
|
preconditioners only);
|
|
|
|
|
\item the smoother of the multi-level preconditioners, or the one-level
|
|
|
|
|
\item the smoother of the multilevel preconditioners, or the one-level
|
|
|
|
|
preconditioner.
|
|
|
|
|
|
|
|
|
|
\end{enumerate}
|
|
|
|
|
@ -237,20 +237,20 @@ solver is changed to the default sequential solver.
|
|
|
|
|
\hline
|
|
|
|
|
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
|
|
|
|
|
\textsc{comments} \\ \hline
|
|
|
|
|
%\multicolumn{5}{|c|}{\emph{type of the multi-level preconditioner}}\\ \hline
|
|
|
|
|
%\multicolumn{5}{|c|}{\emph{type of the multilevel preconditioner}}\\ \hline
|
|
|
|
|
%\verb|mld_ml_cycle_| \par
|
|
|
|
|
\verb|'ML_CYCLE'| & \verb|character(len=*)|
|
|
|
|
|
& \texttt{'VCYCLE'} \par \texttt{'WCYCLE'} \par \texttt{'KCYCLE'} \par
|
|
|
|
|
\texttt{'MULT'} \par \texttt{'ADD'}
|
|
|
|
|
& \texttt{'VCYCLE'}
|
|
|
|
|
&Multi-level cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz,
|
|
|
|
|
&Multilevel cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz,
|
|
|
|
|
and Additive Schwarz. \par
|
|
|
|
|
Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
|
|
|
|
|
is included for compatibility with previous versions of MLD2P4. \\ \hline
|
|
|
|
|
%\verb|mld_outer_sweeps_| \par
|
|
|
|
|
\verb|'OUTER_SWEEPS'| & \texttt{integer} &
|
|
|
|
|
Any integer \par number $\ge 1$ & 1 &
|
|
|
|
|
Number of multi-level cycles. \\ \hline
|
|
|
|
|
Number of multilevel cycles. \\ \hline
|
|
|
|
|
%\verb|mld_smoother_type_| \par \verb|SMOOTHER_TYPE| & \verb|character(len=*)|
|
|
|
|
|
% & \texttt{'JACOBI'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'}
|
|
|
|
|
% & \texttt{'AS'}
|
|
|
|
|
@ -264,7 +264,7 @@ solver is changed to the default sequential solver.
|
|
|
|
|
%\hline
|
|
|
|
|
\end{tabular}
|
|
|
|
|
\end{center}
|
|
|
|
|
\caption{Parameters defining the multi-level cycle and the number of cycles to
|
|
|
|
|
\caption{Parameters defining the multilevel cycle and the number of cycles to
|
|
|
|
|
be applied.
|
|
|
|
|
\label{tab:p_cycle}}
|
|
|
|
|
\esideways
|
|
|
|
|
@ -448,12 +448,11 @@ the parameter \texttt{ilev}.} \\
|
|
|
|
|
Note that \texttt{UMF} and \texttt{SLU} require the coarsest
|
|
|
|
|
matrix to be replicated, \texttt{SLUDIST}, \texttt{JACOBI},
|
|
|
|
|
\texttt{GS} and \texttt{BJAC} require it to be
|
|
|
|
|
distributed, \texttt{MUMPS} can be used with either
|
|
|
|
|
distributed, and \texttt{MUMPS} 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
|
|
|
|
|
value UMFPACK and SuperLU\_Dist
|
|
|
|
|
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
|
|
|
|
|
%\verb|mld_coarse_subsolve_| \par
|
|
|
|
|
\verb|'COARSE_SUBSOLVE'| & \verb|character(len=*)|
|
|
|
|
|
@ -527,7 +526,7 @@ level (continued).\label{tab:p_coarse_1}}
|
|
|
|
|
& \verb|'JACOBI'| \par \verb|'GS'| \par \verb|'BGS'| \par \verb|'BJAC'|
|
|
|
|
|
\par \verb|'AS'|
|
|
|
|
|
& \verb|'FBGS'|
|
|
|
|
|
& Type of smoother used in the multi-level preconditioner:
|
|
|
|
|
& Type of smoother used in the multilevel preconditioner:
|
|
|
|
|
point-Jacobi, hybrid (forward) Gauss-Seidel,
|
|
|
|
|
hybrid backward Gauss-Seidel, block-Jacobi, and
|
|
|
|
|
Additive Schwarz. \par
|
|
|
|
|
@ -539,7 +538,7 @@ level (continued).\label{tab:p_coarse_1}}
|
|
|
|
|
\texttt{'ILUT'} \par \texttt{'MILU'} \par
|
|
|
|
|
\par \texttt{'MUMPS'} \par \texttt{'SLU'} \par \texttt{'UMF'}
|
|
|
|
|
& \texttt{GS} and \texttt{BGS} for pre- and post-smoothers
|
|
|
|
|
of multi-level preconditioners, respectively \par
|
|
|
|
|
of multilevel preconditioners, respectively \par
|
|
|
|
|
\texttt{ILU} for block-Jacobi and Additive Schwarz
|
|
|
|
|
one-level preconditioners
|
|
|
|
|
& The local solver to be used with the smoother or one-level
|
|
|
|
|
@ -554,7 +553,7 @@ level (continued).\label{tab:p_coarse_1}}
|
|
|
|
|
& Any integer \par number~$\ge 0$
|
|
|
|
|
& 1
|
|
|
|
|
& Number of sweeps of the smoother or one-level preconditioner.
|
|
|
|
|
In the multi-level case, no pre-smother or
|
|
|
|
|
In the multilevel case, no pre-smother or
|
|
|
|
|
post-smoother is used if this parameter is set to 0
|
|
|
|
|
together with \verb|pos='PRE'| or \verb|pos='POST|,
|
|
|
|
|
respectively. \\ \hline
|
|
|
|
|
@ -635,7 +634,7 @@ level (continued).\label{tab:p_coarse_1}}
|
|
|
|
|
\noindent
|
|
|
|
|
This routine builds the one-level preconditioner \verb|p| according to the requirements
|
|
|
|
|
made by the user through the routines \verb|init| and \verb|set|
|
|
|
|
|
(see Sections~\ref{sec:hier_bld} and~\ref{sec:smooth_bld} for multi-level preconditioners).
|
|
|
|
|
(see Sections~\ref{sec:hier_bld} and~\ref{sec:smooth_bld} for multilevel preconditioners).
|
|
|
|
|
|
|
|
|
|
{\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip
|
|
|
|
|
|
|
|
|
|
@ -664,7 +663,7 @@ as follows:
|
|
|
|
|
\end{center}
|
|
|
|
|
|
|
|
|
|
\noindent
|
|
|
|
|
In this case, the routine can be used to build multi-level preconditioners too.
|
|
|
|
|
In this case, the routine can be used to build multilevel preconditioners too.
|
|
|
|
|
|
|
|
|
|
\clearpage
|
|
|
|
|
|
|
|
|
|
@ -676,7 +675,7 @@ In this case, the routine can be used to build multi-level preconditioners too.
|
|
|
|
|
|
|
|
|
|
\noindent
|
|
|
|
|
This routine builds the hierarchy of matrices and restriction/prolongation
|
|
|
|
|
operators for the multi-level preconditioner \verb|p|, according to the requirements
|
|
|
|
|
operators for the multilevel preconditioner \verb|p|, according to the requirements
|
|
|
|
|
made by the user through the routines \verb|init| and \verb|set|.
|
|
|
|
|
|
|
|
|
|
{\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip
|
|
|
|
|
@ -710,7 +709,7 @@ single/double precision version of MLD2P4 under use.
|
|
|
|
|
|
|
|
|
|
\noindent
|
|
|
|
|
This routine builds the smoothers and the coarsest-level solvers for the
|
|
|
|
|
multi-level preconditioner \verb|p|, according to the requirements made by
|
|
|
|
|
multilevel preconditioner \verb|p|, according to the requirements made by
|
|
|
|
|
the user through the routines \verb|init| and \verb|set|, and based on the aggregation
|
|
|
|
|
hierarchy produced by a previous call to \verb|hierarchy_build|
|
|
|
|
|
(see Section~\ref{sec:hier_bld}).
|
|
|
|
|
|
Daniela di Serafino
7 years ago