stopcriterion
			
			
		
Salvatore Filippone 17 years ago
parent 5cad1f94bb
commit 797d7f4193

@ -85,8 +85,9 @@
TOPFILE = userguide.tex TOPFILE = userguide.tex
SECFILE = title.tex abstract.tex overview.tex conventions.tex distribution.tex \ SECFILE = title.tex abstract.tex overview.tex conventions.tex distribution.tex \
building.tex gettingstarted.tex advanced.tex errors.tex \ building.tex background.tex gettingstarted.tex userinterface.tex \
listofroutines.tex bibliography.tex userinterface.tex background.tex errors.tex bibliography.tex license.tex
# advanced.tex listofroutines.tex
FIGDIR = figures FIGDIR = figures
XPDFFLAGS = XPDFFLAGS =

@ -5,7 +5,7 @@ It implements various versions of one-level additive and of multi-level additive
and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach
is applied to generate coarse-level corrections, so that no geometric background is needed is applied to generate coarse-level corrections, so that no geometric background is needed
concerning the matrix to be preconditioned. The matrix is required to be square, real concerning the matrix to be preconditioned. The matrix is required to be square, real
or complex, with a symmetric sparsity pattern or complex, with a symmetric sparsity pattern.
MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the
context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms)
@ -14,12 +14,9 @@ available in this framework. MLD2P4 enables the user to easily specify different
of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search
for the ``best'' preconditioner for the problem at hand. The package has been designed for the ``best'' preconditioner for the problem at hand. The package has been designed
employing object-oriented techniques, using Fortran 95 and MPI, with interfaces to employing object-oriented techniques, using Fortran 95 and MPI, with interfaces to
additional external libraries such as UMFPACK, SuperLU and SuperLU\_Dist, that additional third party libraries such as UMFPACK, SuperLU and SuperLU\_Dist, that
can be exploited in building multi-level preconditioners. can be exploited in building multi-level preconditioners.
The software is freely distributable, under the terms of the license
in Appendix~\ref{sec:distribution}.
This guide provides a brief description of the functionalities and This guide provides a brief description of the functionalities and
the user interface of MLD2P4. the user interface of MLD2P4.
\end{abstract} \end{abstract}

@ -1,6 +1,6 @@
\section{Multi-level Domain Decomposition Background\label{sec:background}} \section{Multi-level Domain Decomposition Background\label{sec:background}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:background} Background}} {\textsc{\ref{sec:background} Multi-level Domain Decomposition Background}}
\emph{Domain Decomposition} (DD) preconditioners, coupled with Krylov iterative \emph{Domain Decomposition} (DD) preconditioners, coupled with Krylov iterative
solvers, are widely used in the parallel solution of large and sparse linear systems. solvers, are widely used in the parallel solution of large and sparse linear systems.
@ -17,7 +17,7 @@ solution of the original problem from the local solutions
\emph{Additive Schwarz} preconditioners are DD preconditioners using overlapping \emph{Additive Schwarz} preconditioners are DD preconditioners using overlapping
submatrices, i.e.\ with some common rows, to couple the local information submatrices, i.e.\ with some common rows, to couple the local information
related to the submatrices (see, e.g., \cite{dd2_96}). related to the submatrices (see, e.g., \cite{dd2_96}).
The main motivations for choosing Additive Schwarz preconditioners are their The main motivation for choosing Additive Schwarz preconditioners is their
intrinsic parallelism. A drawback of these intrinsic parallelism. A drawback of these
preconditioners is that the number of iterations of the preconditioned solvers preconditioners is that the number of iterations of the preconditioned solvers
generally grows with the number of submatrices. This may be a serious limitation generally grows with the number of submatrices. This may be a serious limitation
@ -29,16 +29,16 @@ in a coarse space, which globally couples the information related to the single
submatrices. submatrices.
\emph{Two-level Schwarz} preconditioners are obtained \emph{Two-level Schwarz} preconditioners are obtained
by combining basic (one-level) Schwarz preconditioners with coarse-level by combining basic (one-level) Schwarz preconditioners with a coarse-level
corrections. In this context, the one-level preconditioner is often correction. In this context, the one-level preconditioner is often
called smoother. Different two-level preconditioners are obtained by varying the called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother, of the coarse-level correction and the choice of the smoother and of the coarse-level correction, and the
way they are combined \cite{dd2_96}. The same reasoning can be applied starting way they are combined \cite{dd2_96}. The same reasoning can be applied starting
from the coarse-level system, i.e.\ a coarse-space correction can be built from the coarse-level system, i.e.\ a coarse-space correction can be built
from this system, thus obtaining \emph{multi-level} preconditioners. from this system, thus obtaining \emph{multi-level} preconditioners.
It is worth noting that optimal preconditioners do not necessarily correspond It is worth noting that optimal preconditioners do not necessarily correspond
to minimum execution times. Indeed, to obtain effective multilevel preconditioners to minimum execution times. Indeed, to obtain effective multi-level preconditioners
a tradeoff between optimality of convergence and the cost of building and applying a tradeoff between optimality of convergence and the cost of building and applying
the coarse-space corrections must be achieved. The choice of the number of levels, the coarse-space corrections must be achieved. The choice of the number of levels,
i.e.\ of the coarse-space corrections, also affects the effectiveness of the i.e.\ of the coarse-space corrections, also affects the effectiveness of the
@ -74,7 +74,7 @@ we first provide a sketch of the AS preconditioners.
Given the linear system \Ref{system1}, Given the linear system \Ref{system1},
where $A=(a_{ij}) \in \Re^{n \times n}$ is a where $A=(a_{ij}) \in \Re^{n \times n}$ is a
nonsingular sparse matrix with a symmetric non-zero pattern, nonsingular sparse matrix with a symmetric nonzero pattern,
let $G=(W,E)$ be the adjacency graph of $A$, where $W=\{1, 2, \ldots, n\}$ let $G=(W,E)$ be the adjacency graph of $A$, where $W=\{1, 2, \ldots, n\}$
and $E=\{(i,j) : a_{ij} \neq 0\}$ are the vertex set and the edge set of $G$, and $E=\{(i,j) : a_{ij} \neq 0\}$ are the vertex set and the edge set of $G$,
respectively. Two vertices are called adjacent if there is an edge connecting respectively. Two vertices are called adjacent if there is an edge connecting
@ -84,7 +84,7 @@ Given a 0-overlap (or non-overlapping) partition of $W$,
i.e.\ a set of $m$ disjoint nonempty sets $W_i^0 \subset W$ such that i.e.\ a set of $m$ disjoint nonempty sets $W_i^0 \subset W$ such that
$\cup_{i=1}^m W_i^0 = W$, a $\delta$-overlap $\cup_{i=1}^m W_i^0 = W$, a $\delta$-overlap
partition of $W$ is obtained by considering the sets partition of $W$ is obtained by considering the sets
$W_i^\delta \supset W_i^{\delta-1}$, obtained by including the vertices that $W_i^\delta \supset W_i^{\delta-1}$ obtained by including the vertices that
are adjacent to any vertex in $W_i^{\delta-1}$. are adjacent to any vertex in $W_i^{\delta-1}$.
Let $n_i^\delta$ be the size of $W_i^\delta$ and $R_i^{\delta} \in Let $n_i^\delta$ be the size of $W_i^\delta$ and $R_i^{\delta} \in
@ -107,12 +107,16 @@ to a vector $v \in \Re^n$ within a Krylov solver requires the following
three steps: three steps:
\begin{enumerate} \begin{enumerate}
\item restriction of $v$ as $v_i = R_i^{\delta} v$, $i=1,\ldots,m$; \item restriction of $v$ as $v_i = R_i^{\delta} v$, $i=1,\ldots,m$;
\item (approximate) solution of the linear systems $A_i^\delta w_i = v_i$, \item solution of the linear systems $A_i^\delta w_i = v_i$,
$i=1,\ldots,m$; $i=1,\ldots,m$;
\item prolongation and sum of the $w_i$'s, i.e. $w = \sum_{i=1}^m (R_i^{\delta})^T w_i$. \item prolongation and sum of the $w_i$'s, i.e. $w = \sum_{i=1}^m (R_i^{\delta})^T w_i$.
\end{enumerate} \end{enumerate}
Note that the linear systems at step 2 are usually solved approximately,
e.g.\ using incomplete LU factorizations such as ILU($p$), MILU($p$) and
ILU($p,t$) \cite[Chapter 10]{Saad_book}.
A variant of the classical AS preconditioner that outperforms it A variant of the classical AS preconditioner that outperforms it
in terms of both convergence rate and of computation and communication in terms of convergence rate and of computation and communication
time on parallel distributed-memory computers is the so-called \emph{Restricted AS time on parallel distributed-memory computers is the so-called \emph{Restricted AS
(RAS)} preconditioner~\cite{CAI_SARKIS,EFSTATHIOU}. It (RAS)} preconditioner~\cite{CAI_SARKIS,EFSTATHIOU}. It
is obtained by zeroing the components of $w_i$ corresponding to the is obtained by zeroing the components of $w_i$ corresponding to the
@ -207,16 +211,21 @@ On the other hand, the use of few processors often leads to local sumatrices tha
are too expensive to be processed on single processors, because of memory and/or are too expensive to be processed on single processors, because of memory and/or
computing requirements. Therefore, it seems natural to use a recursive approach, computing requirements. Therefore, it seems natural to use a recursive approach,
in which the coarse-level correction is re-applied starting from the current in which the coarse-level correction is re-applied starting from the current
coarse-level system. The corresponding preconditioners are called \emph{multi-level}. coarse-level system. The corresponding preconditioners, called \emph{multi-level}
One more reason for the multi-level approach is that it may significantly preconditioners, can significantly reduce the computational cost of preconditioning
reduce the computational cost of preconditioning with respect to the two-level case with respect to the two-level case (see \cite[Chapter 3]{dd2_96}).
(see \cite[Chapter 3]{dd2_96}). Additive and hybrid multilevel preconditioners Additive and hybrid multilevel preconditioners
are obtained as direct extensions of the two-level counterparts. are obtained as direct extensions of the two-level counterparts.
The algorithm for applying a multi-level version of the two-level hybrid For a detailed descrition of them, the reader is
post-smoothed preconditioner is reported in Figure~\ref{fig:mlhpost_alg}.
Other combinations of the smoothers and coarse-level corrections are possible, leading to variants
of the previous algorithms. For a detailed descrition of them, the reader is
referred to \cite[Chapter 3]{dd2_96}. referred to \cite[Chapter 3]{dd2_96}.
The algorithm for the application of a multi-level hybrid
post-smoothed preconditioner $M$ to a vector $v$, i.e.\ for the
computation of $w=M^{-1}v$ is reported, for
example, in Figure~\ref{fig:mlhpost_alg}. Here the number of levels
is denoted by $nlev$ and the levels are numbered in increasing order starting
from the finest one, i.e.\ the finest level is level 1; the coarse matrix
and the corresponding basic preconditioner at each level $l$ are denoted by $A_l$ and
$M_l$, respectively, with $A_1=A$.
% %
\begin{figure}[t] \begin{figure}[t]
\begin{center} \begin{center}
@ -224,40 +233,41 @@ referred to \cite[Chapter 3]{dd2_96}.
\begin{minipage}{.85\textwidth} {\small \begin{minipage}{.85\textwidth} {\small
\begin{tabbing} \begin{tabbing}
\quad \=\quad \=\quad \=\quad \\[-1mm] \quad \=\quad \=\quad \=\quad \\[-1mm]
! assigned the finest matrix\\ %
$A_1 \leftarrow A$;\\[1mm] %! assign the finest matrix\\
! defined the number of levels $nlev$ \\[1mm] %$A_1 \leftarrow A$;\\[1mm]
! defined $nlev-1$ prolongators\\ %! define the number of levels $nlev$ \\[1mm]
$R_l^T, l=2, \ldots, nlev$;\\[1mm] %! define $nlev-1$ prolongators\\
! defined $nlev-1$ coarser matrices\\ %$R_l^T, l=2, \ldots, nlev$;\\[1mm]
$A_l \leftarrow R_lA_{l-1}R_l^T, \; l=2, \ldots, nlev$;\\[1mm] %! define $nlev-1$ coarser matrices\\
! defined the $nlev-1$ basic Schwarz preconditioners\\ %$A_l \leftarrow R_lA_{l-1}R_l^T, \; l=2, \ldots, nlev$;\\[1mm]
$M_l$, basic preconditioner for $A_l \; l=1, \ldots, nlev-1$;\\[1mm] %! define the $nlev-1$ basic Schwarz preconditioners\\
! assigned a vector $v$\\ %$M_l$, basic preconditioner for $A_l \; l=1, \ldots, nlev-1$;\\[1mm]
$v_1 \leftarrow v$; \\[2mm] %$! assign a vector $v$\\
%
$v_1 = v$; \\[2mm]
\textbf{for $l=2, nlev$ do}\\[1mm] \textbf{for $l=2, nlev$ do}\\[1mm]
\> ! transfer $v_{l-1}$ to the next coarser level\\ \> ! transfer $v_{l-1}$ to the next coarser level\\
\> $v_l \leftarrow R_lv_{l-1}$; \\[1mm] \> $v_l = R_lv_{l-1}$ \\[1mm]
\textbf{endfor} \\[2mm] \textbf{endfor} \\[2mm]
! apply the coarsest-level correction\\[1mm] ! apply the coarsest-level correction\\[1mm]
$y_{nlev} \leftarrow A_{nlev}^{-1}*v_{nlev}$;\\[2mm] $y_{nlev} = A_{nlev}^{-1} v_{nlev}$\\[2mm]
\textbf{for $l=nlev -1 , 1, -1$ do}\\[1mm] \textbf{for $l=nlev -1 , 1, -1$ do}\\[1mm]
\> ! transfer $y_{l+1}$ to the next finer level\\ \> ! transfer $y_{l+1}$ to the next finer level\\
\> $y_l \leftarrow R_{l+1}^T*y_{l+1}$;\\[1mm] \> $y_l = R_{l+1}^T y_{l+1}$;\\[1mm]
\> ! compute the residual at the current level\\ \> ! compute the residual at the current level\\
\> $r_l \leftarrow v_l-A_l^{-1}*y_l$;\\[1mm] \> $r_l = v_l-A_l^{-1} y_l$;\\[1mm]
\> ! apply the basic Schwarz preconditioner to $r_l$\\ \> ! apply the basic Schwarz preconditioner to the residual\\
\> $r_l \leftarrow M_l^{-1}*r_l$\\[1mm] \> $r_l = M_l^{-1} r_l$\\[1mm]
\> ! update $y_l$\\ \> ! update $y_l$\\
\> $y_l \leftarrow y_l+r_l$\\ \> $y_l = y_l+r_l$\\
\textbf{endfor} \\[1mm] \textbf{endfor} \\[1mm]
! preconditioned vector $w = y_1$;
$w \leftarrow y_1$;
\end{tabbing} \end{tabbing}
} }
\end{minipage} \end{minipage}
} }
\caption{Multi-level hybrid post-smoothed preconditioner.\label{fig:mlhpost_alg}} \caption{Application of the multi-level hybrid post-smoothed preconditioner.\label{fig:mlhpost_alg}}
\end{center} \end{center}
\end{figure} \end{figure}
% %
@ -265,7 +275,7 @@ $w \leftarrow y_1$;
\subsection{Smoothed Aggregation\label{sec:aggregation}} \subsection{Smoothed Aggregation\label{sec:aggregation}}
To define the restriction operator $R_C$, which is used to compute In order to define the restriction operator $R_C$, which is used to compute
the coarse-level matrix $A_C$, MLD2P4 uses the \emph{smoothed aggregation} the coarse-level matrix $A_C$, MLD2P4 uses the \emph{smoothed aggregation}
algorithm described in \cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}. algorithm described in \cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}.
The basic idea of this algorithm is to build a coarse set of vertices The basic idea of this algorithm is to build a coarse set of vertices
@ -283,16 +293,15 @@ Three main steps can be identified in the smoothed aggregation procedure:
%\textbf{NOTA: Controllare cosa fa trilinos dopo il primo passo.} %\textbf{NOTA: Controllare cosa fa trilinos dopo il primo passo.}
To perform the coarsening step, we have implemented the aggregation algorithm sketched To perform the coarsening step, we have implemented the aggregation algorithm sketched
in \cite{apnum_07}. According to \cite{BREZINA_VANEK}, a modification of this algorithm in \cite{apnum_07}. According to \cite{VANEK_MANDEL_BREZINA}, a modification of
has been actually considered, this algorithm has been actually considered,
in which each aggregate $N_r$ is made of vertices of $W$ that are \emph{strongly coupled} in which each aggregate $N_r$ is made of vertices of $W$ that are \emph{strongly coupled}
to a certain root vertex $r \in W$, i.e.\ to a certain root vertex $r \in W$, i.e.\
\[ N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\} \[ N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\}
\cup \left\{ r \right\} , \cup \left\{ r \right\} ,
\] \]
for a given $\theta \in [0,1]$. \textbf{L'ALGORITMO USA IL MAGGIORE STRETTO? ALTRIMENTI for a given $\theta \in [0,1]$.
CON THETA=0 AGGREGHIAMO ANCHE I VERTICI CON COEFFICIENTE CORRISPONDENTE NULLO} Since this algorithm has a sequential nature, a \emph{decoupled} version of
Since the previous algorithm has a sequential nature, a \emph{decoupled} version of
it has been chosen, where each processor $i$ independently applies the algorithm to it has been chosen, where each processor $i$ independently applies the algorithm to
the set of vertices $W_i^0$ assigned to it in the initial data distribution. This the set of vertices $W_i^0$ assigned to it in the initial data distribution. This
version is embarrassingly parallel, since it does not require any data communication. version is embarrassingly parallel, since it does not require any data communication.

@ -1,7 +1,8 @@
\section{Bibliography\label{sec:bib}} %\section{Bibliography\label{sec:bib}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:bib} Bibliography}} {\textsc{References}}
\let\refname\relax
%\let\refname\relax
\begin{thebibliography}{99} \begin{thebibliography}{99}
% %
@ -146,6 +147,11 @@ ACM Transactions on Mathematical Software, 29, 2, 2003, 110--140.
%{\em Fortran 95/2003 explained.} %{\em Fortran 95/2003 explained.}
%{Oxford University Press}, 2004. %{Oxford University Press}, 2004.
% %
\bibitem{Saad_book}
Y.~Saad,
\emph{Iterative methods for sparse linear systems}, 2nd edition,
SIAM, 2003
\bibitem{dd2_96} \bibitem{dd2_96}
B.~Smith, P.~Bjorstad, W.~Gropp, B.~Smith, P.~Bjorstad, W.~Gropp,
{\em Domain Decomposition: Parallel Multilevel Methods for Elliptic {\em Domain Decomposition: Parallel Multilevel Methods for Elliptic

@ -1,9 +1,13 @@
\section{Configuring and Building MLD2P4\label{sec:configuring}} \section{Configuring and Building MLD2P4\label{sec:building}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:configuring} Configuring and Building}} {\textsc{\ref{sec:building} Configuring and Building MLD2P4}}
- uso di GNU autoconf e automake \\ - uso di GNU autoconf e automake, con riferimento alla compilazione delle varie versioni
- software di base necessario (MPI, BLACS, BLAS, PSBLAS, UMFPACK ? - specificare versioni)\\ (reale/complessa, singola/doppia precisione) \\
- software opzionale (SuperLU, SuperLUdist - specificare versioni e opzioni di configure)\\ - software di base (MPI, BLACS, BLAS, PSBLAS - specificare versioni)\\
- sistemi operativi e compilatori su cui MLD2P4 e' stato costruito con successo \\ - software `third party" (UMFPACK, SuperLU, SuperLUdist - specificare versioni e opzioni di
configure, dire che UMFPACK e SuperLU sono richiesti, rispettivamente, dalle versioni in
singola ed in doppia precisione.)\\
- sistemi operativi e compilatori su cui MLD2P4 e' stato implementato con successo \\
- sono previste opzioni di configurazione per il debugging o per il profiling? \\ - sono previste opzioni di configurazione per il debugging o per il profiling? \\
- albero delle directory generato al momento dell'installazione\\ - albero delle directory generato al momento dell'installazione, con brevissima
descrizione del contenuto delle directory - aggiungere la directory \texttt{examples}\\

@ -1,8 +1,8 @@
\section{Notational Conventions\label{sec:conventions}} \section{Notational Conventions\label{sec:conventions}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:conventions} Notational conventions}} {\textsc{\ref{sec:conventions} Notational Conventions}}
- caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec) \\ - caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec) \\
- convenzioni sui nomi di routine (differenza nei nomi tra high-level e medium-level), - convenzioni sui nomi di routine (anche differenza nei nomi tra high-level e
strutture dati, moduli, costanti, etc. (vedi guida psblas) \\ medium-level?), strutture dati, moduli, costanti, etc. (vedi guida psblas) \\
- versione reale e complessa, singola e doppia precisione\\ - versione reale e complessa, singola e doppia precisione\\

@ -1,44 +1,7 @@
\section{License\label{sec:distribution}} \section{Code Distribution\label{sec:distribution}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:distribution} License}} {\textsc{\ref{sec:distribution} Code Distribution}}
The MLD2P4 is freely distributable under the following copyright \noindent
terms: {\small - sito web sul quale e' disponibile il software\\
\begin{verbatim} - modalita' di uso con cenno alla licenza (i dettagli sulla licenza vanno in appendice)
MLD2P4 version 1.0
MultiLevel Domain Decomposition Parallel Preconditioners Package
based on PSBLAS (Parallel Sparse BLAS version 2.3)
(C) Copyright 2008
Salvatore Filippone University of Rome Tor Vergata
Alfredo Buttari University of Rome Tor Vergata
Pasqua D'Ambra ICAR-CNR, Naples
Daniela di Serafino Second University of Naples
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the MLD2P4 group or the names of its contributors may
not be used to endorse or promote products derived from this
software without specific written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
\end{verbatim}
}

@ -1,6 +1,6 @@
\section{Error Handling}\label{sec:errors} \section{Error Handling}\label{sec:errors}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:errors} Error handling}} {\textsc{\ref{sec:errors} Error handling}}
Error handling Error handling
- Breve descrizione con rinvio alla guida di PSBLAS - Breve descrizione con rinvio alla guida di PSBLAS

@ -1,6 +1,6 @@
\section{Getting Started\label{sec:started}} \section{Getting Started\label{sec:started}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:started} Getting started}} {\textsc{\ref{sec:started} Getting Started}}
We describe the basics for building and applying MLD2P4 one-level and multi-level We describe the basics for building and applying MLD2P4 one-level and multi-level
Schwarz preconditioners with the Krylov solvers included in PSBLAS \cite{PSBLASGUIDE}. Schwarz preconditioners with the Krylov solvers included in PSBLAS \cite{PSBLASGUIDE}.
@ -17,15 +17,16 @@ The following steps are required:
a preconditioner type chosen by the user}. This is performed by the routine a preconditioner type chosen by the user}. This is performed by the routine
\verb|mld_precinit|, which also sets defaults for each preconditioner \verb|mld_precinit|, which also sets defaults for each preconditioner
type selected by the user. The defaults associated to each preconditioner type selected by the user. The defaults associated to each preconditioner
type are listed in Table~\ref{tab:precinit}, where the strings used by type are given in Table~\ref{tab:precinit}, where the strings used by
\verb|mld_precinit| to identify the preconditioner types are also given. \verb|mld_precinit| to identify the preconditioner types are also given.
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
\item \emph{Modify the selected preconditioner type, by properly setting \item \emph{Modify the selected preconditioner type, by properly setting
preconditioner parameters.} This is performed by the routine \verb|mld_precset|. preconditioner parameters.} This is performed by the routine \verb|mld_precset|.
This routine must be called only if the user wants to modify the default values This routine must be called only if the user wants to modify the default values
of the parameters associated to the selected preconditioner type, to obtain a variant of the parameters associated to the selected preconditioner type, to obtain a variant
of the preconditioner. of the preconditioner. Examples of use of \verb|mld_precset| are given in
Examples of use of \verb|mld_precset| is given in Section~\ref{sec:examples}; Section~\ref{sec:examples}; a complete list of all the
a complete list of all the
preconditioner parameters and their allowed and default values is provided in preconditioner parameters and their allowed and default values is provided in
Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}. Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
\item \emph{Build the preconditioner for a given matrix.} This is performed by \item \emph{Build the preconditioner for a given matrix.} This is performed by
@ -39,39 +40,43 @@ The following steps are required:
be performed when the preconditioner is no more used. be performed when the preconditioner is no more used.
\end{enumerate} \end{enumerate}
A detailed description of the above routines is given in Section~\ref{sec:userinterface}. A detailed description of the above routines is given in Section~\ref{sec:userinterface}.
Note that the Fortran 95 module \verb|mld_prec_mod| must be used in the program
calling the MLD2P4 routines; this requires also the use of the
\verb|psb_base_mod| for the sparse matrix and communication descriptor
data types, as well as for the kind parameters for vectors, and the
use of the module \verb|psb_krylov_mod| for interfacing with the
Krylov solvers. Note that the include path for MLD2P4 must override
those for the base PSBLAS, e.g. they must come first in the sequence
passed to the compiler, as the MLD2P4 version of the Krylov interfaces
must override that of PSBLAS. This will change in the future when the
support for the \verb|class| statement becomes widespread in Fortran
compilers.
Examples showing the basic use of MLD2P4 are reported in Section~\ref{sec:examples}. Examples showing the basic use of MLD2P4 are reported in Section~\ref{sec:examples}.
\noindent Note that the Fortran 95 module \verb|mld_prec_mod|, containing the definition of the
\textbf{Remark.} The coarsest-level solver used by the default two-level preconditioner data type and the interfaces to the routines of MLD2P4,
must be used in any program calling such routines.
The modules \verb|psb_base_mod|, for the sparse matrix and communication descriptor
data types, and \verb|psb_krylov_mod|, for interfacing with the
Krylov solvers, must be also used (see Section~\ref{sec:examples}).
\ \\
\textbf{Remark 1.} The coarsest-level solver used by the default two-level
preconditioner has been chosen by taking into account that, on parallel preconditioner has been chosen by taking into account that, on parallel
machines, it often leads to the smallest execution time when applied to machines, it often leads to the smallest execution time when applied to
linear systems coming from finite-difference discretizations of basic linear systems coming from finite-difference discretizations of basic
elliptic PDE problems, considered as standard tests for multi-level Schwarz elliptic PDE problems, considered as standard tests for multi-level Schwarz
preconditioners \cite{aaecc_07,apnum_07}. However, this solver does preconditioners \cite{aaecc_07,apnum_07}. However, this solver does
not necessarily to the smallest number of iterations of the not necessarily correspond to the smallest number of iterations of the
preconditioned Krylov method, which is usually obtained by applying a preconditioned Krylov method, which is usually obtained by applying a
direct solver, e.g.\ based on the LU factorization, on a matrix a direct solver to the coarsest-level system, e.g.\ based on the LU
replicated at the coarsest level (see Section~\ref{sec:userinterface} factorization (see Section~\ref{sec:userinterface}
for coarsest-level solvers available in MLD2P4). for the coarsest-level solvers available in MLD2P4).
\ \\
\textbf{Remark 2.} The include path for MLD2P4 must override
those for PSBLAS, e.g.\ the latter must come first in the sequence
passed to the compiler, as the MLD2P4 version of the Krylov solver
interfaces must override that of PSBLAS. This will change in the future
when the support for the \verb|class| statement becomes widespread in Fortran
compilers.
\begin{table}[th] \begin{table}[th]
{
\begin{center} \begin{center}
\begin{tabular}{|l|l|p{6.7cm}|} %{\small
\begin{tabular}{|l|l|p{6.4cm}|}
\hline \hline
\emph{Type} & \emph{String} & \emph{Default preconditioner} \\ \hline \textsc{type} & \textsc{string} & \textsc{default preconditioner} \\ \hline
No preconditioner &\verb|'NOPREC'|& (Considered only to use the PSBLAS No preconditioner &\verb|'NOPREC'|& (Considered only to use the PSBLAS
Krylov solvers with no preconditioner.) \\ Krylov solvers with no preconditioner.) \\
Diagonal & \verb|'DIAG'| & --- \\ Diagonal & \verb|'DIAG'| & --- \\
@ -80,18 +85,23 @@ Additive Schwarz & \verb|'AS'| & Restricted Additive Schwarz (RAS),
with overlap 1 and ILU(0) on the local blocks. \\ with overlap 1 and ILU(0) on the local blocks. \\
Multilevel &\verb|'ML'| & Multi-level hybrid preconditioner (additive on the Multilevel &\verb|'ML'| & Multi-level hybrid preconditioner (additive on the
same level and multiplicative through the levels), same level and multiplicative through the levels),
with post-smoothing only. Number of levels: 2; with post-smoothing only.
post-smoother: RAS with overlap 1 and with ILU(0) Number of levels: 2.
on the local blocks; coarsest matrix: distributed Post-smoother: RAS with overlap 1 and ILU(0)
among the processors; (approximate) coarse-level on the local blocks.
solver: 4 sweeps of the block-Jacobi solver, Aggregation: smoothed aggregation with
with the UMFPACK LU factorization threshold $\theta = 0$.
on the blocks (double precision versions) or Coarsest matrix: distributed among the processors.
\textbf{XXXXXXXXX} (single precision versions)\\ Coarse-level solver:
4 sweeps of the block-Jacobi solver,
with LU factorization of the blocks
(UMFPACK for the double precision versions and
SuperLU for the single precision ones) \\
\hline \hline
\end{tabular} \end{tabular}
%}
\end{center} \end{center}
}
\caption{Preconditioner types, corresponding strings and default choices. \caption{Preconditioner types, corresponding strings and default choices.
\label{tab:precinit}} \label{tab:precinit}}
\end{table} \end{table}
@ -103,31 +113,32 @@ multi-level preconditioner available in the real double precision version
of MLD2P4 (see Table~\ref{tab:precinit}). This preconditioner is chosen of MLD2P4 (see Table~\ref{tab:precinit}). This preconditioner is chosen
by simply specifying \verb|'ML'| as second argument of \verb|mld_precinit| by simply specifying \verb|'ML'| as second argument of \verb|mld_precinit|
(a call to \verb|mld_precset| is not needed) and is applied with the BiCGSTAB (a call to \verb|mld_precset| is not needed) and is applied with the BiCGSTAB
solver provided by PSBLAS. The setup and application of the default multi-level solver provided by PSBLAS. As previously observed, the modules \verb|psb_base_mod|,
preconditioners for the real single precision and the complex, single and double \verb|mld_prec_mod| and \verb|psb_krylov_mod| must be used by the example program.
precision, versions are obtained with straightforward modifications of the example.
The part of the code concerning the The part of the code concerning the
reading and assembling of the sparse matrix and the right-hand side vector, performed reading and assembling of the sparse matrix and the right-hand side vector, performed
through the PSBLAS routines for sparse matrix and vector management, is not reported through the PSBLAS routines for sparse matrix and vector management, is not reported
here for brevity; the statements concerning the deallocation of the PSBLAS data structure here for brevity; the statements concerning the deallocation of the PSBLAS
are neglected too. data structure are neglected too.
The complete code can be found in the example program file \verb|example_ml.f90| The complete code can be found in the example program file \verb|mld_dexample_ml.f90|,
in the directory \textbf{XXXXXX (COMPLETARE. DIRE CHE I FILE IN REALTA' SONO DUE, UNO CON in the directory \verb|examples/fileread| of the MLD2P4 tree (see
LA GENERAZIONE DELLA MATRICE ED UNO CON LA LETTURA).} Note that the modules \verb|psb_base_mod| Section~\ref{sec:building}).
and \verb|psb_util_mod| at the beginning of the code are required by PSBLAS. For details on the use of the PSBLAS routines, see the PSBLAS User's
\textbf{O psb\_base\_mod} E' RICHIESTO ANCHE DA MLD2P4?) Guide \cite{PSBLASGUIDE}.
For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite{PSBLASGUIDE}.
\textbf{LE FIGURE SONO DECENTRATE, NONOSTANTE IL CENTER. CI VUOLE UNA MINIPAGE?} The setup and application of the default multi-level
preconditioners for the real single precision and the complex, single and double
precision, versions are obtained with straightforward modifications of the previous
example (see Section~\ref{sec:userinterface} for details). If these versions are installed,
the corresponding Fortran 95 codes are available in \verb|examples/fileread/| with these.
\begin{figure}[tbp] \begin{figure}[tbp]
\begin{center} \begin{center}
\begin{minipage}{.90\textwidth}
{\small {\small
\begin{verbatim} \begin{verbatim}
use psb_base_mod use psb_base_mod
use psb_util_mod
use mld_prec_mod use mld_prec_mod
use psb_krylov_mod use psb_krylov_mod
... ... ... ...
@ -138,6 +149,8 @@ For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite
type(psb_desc_type) :: desc_A type(psb_desc_type) :: desc_A
! preconditioner ! preconditioner
type(mld_dprec_type) :: P type(mld_dprec_type) :: P
! right-hand side and solution vectors
real(kind(1.d0)) :: b(:), x(:)
... ... ... ...
! !
! initialize the parallel environment ! initialize the parallel environment
@ -145,20 +158,18 @@ For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite
call psb_info(ictxt,iam,np) call psb_info(ictxt,iam,np)
... ... ... ...
! !
! read and assemble the matrix A and the right-hand ! read and assemble the matrix A and the right-hand side b
! side b using PSBLAS routines for sparse matrix / ! using PSBLAS routines for sparse matrix / vector management
! vector management
... ... ... ...
! !
! initialize the default multi-level preconditioner, ! initialize the default multi-level preconditioner, i.e. hybrid
! i.e. two-level hybrid Schwarz, using RAS (with ! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks)
! overlap 1 and ILU(0) on the blocks) as post-smoother ! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU
! and 4 block-Jacobi sweeps (with UMFPACK LU on the ! on the blocks) as distributed coarse-level solver
! blocks) as distributed coarse-level solver
call mld_precinit(P,'ML',info) call mld_precinit(P,'ML',info)
! !
! build the preconditioner ! build the preconditioner
call psb_precbld(A,P,desc_A,info) call mld_precbld(A,desc_A,P,info)
! !
! set the solver parameters and the initial guess ! set the solver parameters and the initial guess
... ... ... ...
@ -178,85 +189,94 @@ For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite
stop stop
\end{verbatim} \end{verbatim}
} }
\end{minipage}
\caption{Setup and application of the default multi-level Schwarz preconditioner. \caption{Setup and application of the default multi-level Schwarz preconditioner.
\label{fig:ex_default}} \label{fig:ex_default}}
\end{center} \end{center}
\end{figure} \end{figure}
Different versions of multilevel preconditioner can be obtained by changing Different versions of multi-level preconditioners can be obtained by changing
the default values of the preconditioner parameters. The code reported in the default values of the preconditioner parameters. The code reported in
Figure~\ref{fig:ex_3lh} shows how to set a three-level hybrid Schwarz Figure~\ref{fig:ex_3lh} shows how to set a three-level hybrid Schwarz
preconditioner, which uses block Jacobi with ILU(0) on the preconditioner, which uses block Jacobi with ILU(0) on the
local blocks as post-smoother, a coarsest matrix replicated on the processors, local blocks as post-smoother, has a coarsest matrix replicated on the processors,
and the LU factorization from UMFPACK~\cite{UMFPACK}, version 4.4, as coarse-level solver. and solves the coarsest-level system with the LU factorization from UMFPACK~\cite{UMFPACK}.
The number of levels is specified by using \verb|mld_precinit|; the other The number of levels is specified by using \verb|mld_precinit|; the other
preconditioner parameters are set by calling \verb|mld_precset|. Note that preconditioner parameters are set by calling \verb|mld_precset|. Note that
the type of multilevel framework (i.e.\ multiplicative among the levels the type of multilevel framework (i.e.\ multiplicative among the levels
with post-smoothing only) is not specified since it is the default with post-smoothing only) is not specified since it is the default
set by \verb|mld_precinit|. Figure~\ref{fig:ex_3la} shows how to set by \verb|mld_precinit|.
Figure~\ref{fig:ex_3la} shows how to
set a three-level additive Schwarz preconditioner, set a three-level additive Schwarz preconditioner,
which applies RAS, with overlap 1 and ILU(0) on the blocks, which uses RAS, with overlap 1 and ILU(0) on the blocks,
as pre- and post-smoother, and five block-Jacobi sweeps, with as pre- and post-smoother, and applies five block-Jacobi sweeps, with
the UMFPACK LU factorization on the blocks, as distributed coarsest-level the UMFPACK LU factorization on the blocks, as distributed coarsest-level
solver. Again, \verb|mld_precset| is used only to set solver. Again, \verb|mld_precset| is used only to set
non-default values of the parameters (see Tables~\ref{tab:p_type}-\ref{tab:p_coarse}). non-default values of the parameters (see Tables~\ref{tab:p_type}-\ref{tab:p_coarse}).
In both cases, the construction and the application of the preconditioner In both cases, the construction and the application of the preconditioner
are carried out as for the default multi-level preconditioner. are carried out as for the default multi-level preconditioner.
The code fragments shown in in Figures~\ref{fig:ex_3lh}-\ref{fig:ex_3la} are The code fragments shown in in Figures~\ref{fig:ex_3lh}-\ref{fig:ex_3la} are
included in the example program file \verb|example_ml.f90|. included in the example program file \verb|mld_dexample_ml.f90| too.
\textbf{LO STESSO PROGRAMMA CONTIENE I TRE ESEMPI, CON UN SWITCH TRA L'UNO E L'ALTRO
O FACCIAMO 3 PROGRAMMI DISTINTI? NON RICORDO CHE COSA ABBIAMO DECISO.
PASQUA: ABBIAMO DETTO CHE ERA PREFERIBILE UN UNICO PROGRAMMA CON SWITCH.}
Finally, Figure~\ref{fig:ex_1l} shows the setup of a one-level Finally, Figure~\ref{fig:ex_1l} shows the setup of a one-level
additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding code, additive Schwarz preconditioner, i.e.\ RAS with overlap 2. The corresponding
including also the application of the preconditioner is in the example example program is available in \verb|mld_dexample_1lev.f90|.
program file \verb|example_1lev.f90|.
\begin{figure}[tbp] For all the previous preconditioners, example programs where the sparse matrix and
the right-hand side are generated by discretizing a Poisson equation with Dirichlet
boundary conditions are also available in the directory \verb|examples/pdegen|.
\begin{figure}[tbh]
\begin{center} \begin{center}
\begin{minipage}{.90\textwidth}
{\small {\small
\begin{verbatim} \begin{verbatim}
... ... ... ...
! set a three-level hybrid Schwarz preconditioner, ! set a three-level hybrid Schwarz preconditioner, which uses
! which uses block Jacobi (with ILU(0) on the blocks) ! block Jacobi (with ILU(0) on the blocks) as post-smoother,
! as post-smoother, a coarsest matrix replicated on the ! a coarsest matrix replicated on the processors, and the
! processors, and the LU factorization from UMFPACK ! LU factorization from UMFPACK as coarse-level solver
! as coarse-level solver
call mld_precinit(P,'ML',info,nlev=3) call mld_precinit(P,'ML',info,nlev=3)
call_mld_precset(P,mld_smoother_type_,'BJAC',info) call_mld_precset(P,mld_smoother_type_,'BJAC',info)
call mld_precset(P,mld_coarse_mat,'REPL') call mld_precset(P,mld_coarse_mat_,'REPL',info)
call mld_precset(P,mld_coarse_solve,'UMF') call mld_precset(P,mld_coarse_solve_,'UMF',info)
... ... ... ...
\end{verbatim} \end{verbatim}
} }
\end{minipage}
\caption{Setup of a hybrid three-level Schwarz preconditioner.\label{fig:ex_3lh}} \caption{Setup of a hybrid three-level Schwarz preconditioner.\label{fig:ex_3lh}}
\end{center} \end{center}
\end{figure} \end{figure}
\begin{figure}[htb] \begin{figure}[tbh]
\begin{center} \begin{center}
\begin{minipage}{.90\textwidth}
{\small {\small
\begin{verbatim} \begin{verbatim}
... ... ... ...
! set a three-level additive Schwarz preconditioner, ! set a three-level additive Schwarz preconditioner, which uses
! which uses RAS (with overlap 1 and ILU(0) on the blocks) ! RAS (with overlap 1 and ILU(0) on the blocks) as pre- and
! as pre- and post-smoother, and 5 block-Jacobi sweeps ! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
! (with UMFPACK LU on the blocks) as distributed ! on the blocks) as distributed coarsest-level solver
! coarsest-level solver
call mld_precinit(P,'ML',info,nlev=3) call mld_precinit(P,'ML',info,nlev=3)
call mld_precset(P,mld_ml_type_,'ADD',info) call mld_precset(P,mld_ml_type_,'ADD',info)
call_mld_precset(P,mld_smoother_pos_,'TWOSIDE',info) call_mld_precset(P,mld_smoother_pos_,'TWOSIDE',info)
call mld_precset(P,mld_coarse_sweeps_,5) call mld_precset(P,mld_coarse_sweeps_,5,info)
... ... ... ...
\end{verbatim} \end{verbatim}
} }
\end{minipage}
\caption{Setup of an additive three-level Schwarz preconditioner.\label{fig:ex_3la}} \caption{Setup of an additive three-level Schwarz preconditioner.\label{fig:ex_3la}}
\end{center} \end{center}
\end{figure} \end{figure}
\begin{figure}[htb] \begin{figure}[tbh]
\begin{center} \begin{center}
\begin{minipage}{.90\textwidth}
{\small {\small
\begin{verbatim} \begin{verbatim}
... ... ... ...
@ -266,12 +286,13 @@ program file \verb|example_1lev.f90|.
... ... ... ...
\end{verbatim} \end{verbatim}
} }
\end{minipage}
\caption{Setup of a one-level Schwarz preconditioner.\label{fig:ex_1l}} \caption{Setup of a one-level Schwarz preconditioner.\label{fig:ex_1l}}
\end{center} \end{center}
\end{figure} \end{figure}
\ \\ \ \\
\textbf{Remark.} Any PSBLAS-based program using the basic preconditioners \textbf{Remark 3.} Any PSBLAS-based program using the basic preconditioners
implemented in PSBLAS 2.0, i.e.\ the diagonal and block-Jacobi ones, implemented in PSBLAS 2.0, i.e.\ the diagonal and block-Jacobi ones,
can use the diagonal and block-Jacobi preconditioners can use the diagonal and block-Jacobi preconditioners
implemented in MLD2P4 without any change in the code. implemented in MLD2P4 without any change in the code.

@ -0,0 +1,44 @@
\section{License\label{sec:distribution}}
\markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\textsc{\ref{sec:distribution} License}}
The MLD2P4 is freely distributable under the following copyright
terms: {\small
\begin{verbatim}
MLD2P4 version 1.0
MultiLevel Domain Decomposition Parallel Preconditioners Package
based on PSBLAS (Parallel Sparse BLAS version 2.3)
(C) Copyright 2008
Salvatore Filippone University of Rome Tor Vergata
Alfredo Buttari University of Rome Tor Vergata
Pasqua D'Ambra ICAR-CNR, Naples
Daniela di Serafino Second University of Naples
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the MLD2P4 group or the names of its contributors may
not be used to endorse or promote products derived from this
software without specific written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
\end{verbatim}
}

@ -1,7 +1,6 @@
\section{General Overview\label{sec:overview}} \section{General Overview\label{sec:overview}}
\markboth{\textsc{MLD2P4 User's and Reference Guide}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} {\textsc{\ref{sec:overview} General Overview}}
{\underline{\ref{sec:overview} General Overview}}
The \textsc{Multi-Level Domain Decomposition Parallel Preconditioners Package based on The \textsc{Multi-Level Domain Decomposition Parallel Preconditioners Package based on
PSBLAS (MLD2P4}) provides \emph{multi-level Schwarz preconditioners}~\cite{dd2_96}, PSBLAS (MLD2P4}) provides \emph{multi-level Schwarz preconditioners}~\cite{dd2_96},
@ -31,9 +30,9 @@ as algebraic coarsening strategy~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}.
The package is written in \emph{Fortran~95}, following an The package is written in \emph{Fortran~95}, following an
\emph{object-oriented approach} through the exploitation of features \emph{object-oriented approach} through the exploitation of features
such as abstract data type creation, functional such as abstract data type creation, functional
overloading and dynamic memory management.% , while providing a smooth overloading and dynamic memory management.
% , while providing a smooth
% path towards the integration in legacy application codes. % path towards the integration in legacy application codes.
% \textbf{NON MI PIACE QUESTO PERIODO, E' TROPPO LUNGO. RIUSCITE A SCRIVERLO MEGLIO?}
The parallel implementation is based The parallel implementation is based
on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures. on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures.
Single and double precision implementations of MLD2P4 are available for both the Single and double precision implementations of MLD2P4 are available for both the
@ -42,7 +41,7 @@ real and the complex case, that can be used through a single interface.
MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
in the context of the \emph{PSBLAS (Parallel Sparse BLAS) in the context of the \emph{PSBLAS (Parallel Sparse BLAS)
computational framework}~\cite{psblas_00}. computational framework}~\cite{psblas_00}.
PSBLAS is a library originally developed to address the parallel implementation of PSBLAS is a library originally developed to address the parallel implementation of
iterative solvers for sparse linear system, by providing basic linear algebra iterative solvers for sparse linear system, by providing basic linear algebra
operators and data management facilities for distributed sparse matrices; it operators and data management facilities for distributed sparse matrices; it
@ -71,7 +70,7 @@ by expert users to build new versions of multi-level Schwarz preconditioners.
We provide here a description of the upper-layer routines, but not of the We provide here a description of the upper-layer routines, but not of the
medium-layer ones. medium-layer ones.
This guide is organized as follows: \textbf{ORGANIZZAZIONE DELLA GUIDA} This guide is organized as follows. \textbf{ORGANIZZAZIONE DELLA GUIDA}
%%% Local Variables: %%% Local Variables:
%%% mode: latex %%% mode: latex

@ -1,4 +1,4 @@
\documentclass[a4paper]{article} \documentclass[a4paper,twoside,11pt]{article}
\usepackage{pstricks} \usepackage{pstricks}
\usepackage{fancybox} \usepackage{fancybox}
\usepackage{amsfonts} \usepackage{amsfonts}
@ -112,6 +112,7 @@
\include{overview} \include{overview}
\include{conventions} \include{conventions}
\include{distribution}
\include{building} \include{building}
\include{background} \include{background}
\include{gettingstarted} \include{gettingstarted}
@ -121,12 +122,11 @@
%\include{listofroutines} %\include{listofroutines}
\cleardoublepage \cleardoublepage
\appendix \appendix
\include{distribution} \include{license}
\cleardoublepage \cleardoublepage
\include{bibliography} \include{bibliography}
\end{document} \end{document}
%%% Local Variables: %%% Local Variables:
%%% mode: latex %%% mode: latex

@ -1,12 +1,13 @@
\section{User Interface\label{sec:userinterface}} \section{User Interface\label{sec:userinterface}}
\markboth{\underline{MLD2P4 User's and Reference Guide}} \markboth{\textsc{MLD2P4 User's and Reference Guide}}
{\underline{\ref{sec:userinterface} User Interface}} {\textsc{\ref{sec:userinterface} User Interface}}
The basic user interface of MLD2P4 consists of six routines. The four routines \verb|mld_precinit|, The basic user interface of MLD2P4 consists of six routines. The four routines \verb|mld_precinit|,
\verb|mld_precset|, \verb|mld_precbld| and \verb|mld_precaply| encapsulate all the functionalities for the setup and application of any one-level and multi-level \verb|mld_precset|, \verb|mld_precbld| and \verb|mld_precaply| encapsulate all the functionalities
for the setup and the application of any one-level and multi-level
preconditioner implemented in the package. preconditioner implemented in the package.
The routine \verb|mld_precfree| deallocates the preconditioner data structure, while The routine \verb|mld_precfree| deallocates the preconditioner data structure, while
\verb|mld_precdescr| prints a description of the preconditioner setup by the user. \verb|mld_prec\-descr| prints a description of the preconditioner setup by the user.
For each routine, the same user interface is overloaded with For each routine, the same user interface is overloaded with
respect to the real/complex case and the single/double precision; respect to the real/complex case and the single/double precision;
@ -27,7 +28,8 @@ i.e.
\emph{type}\verb|(|\emph{kind\_parameter}\verb|)|, with \emph{type} = \emph{type}\verb|(|\emph{kind\_parameter}\verb|)|, with \emph{type} =
\verb|real|, \verb|complex| and \emph{kind\_parameter} = \verb|kind(1.e0)|, \verb|real|, \verb|complex| and \emph{kind\_parameter} = \verb|kind(1.e0)|,
\verb|kind(1.d0)|, according to the sparse matrix and preconditioner \verb|kind(1.d0)|, according to the sparse matrix and preconditioner
data structure; note that the PSBLAS module provides the constants \verb|psb_spk_| data structure; note that the PSBLAS module \verb|psb_base_mod|
provides the constants \verb|psb_spk_|
= \verb|kind(1.e0)| and \verb|psb_dpk_| = \verb|kind(1.d0)|; = \verb|kind(1.e0)| and \verb|psb_dpk_| = \verb|kind(1.d0)|;
\item real parameters defining the preconditioner must be declared \item real parameters defining the preconditioner must be declared
according to the precision of the previous data structures according to the precision of the previous data structures
@ -49,19 +51,20 @@ according to the preconditioner type chosen by the user.
\subsubsection*{Arguments} \subsubsection*{Arguments}
\begin{tabular}{p{1.2cm}p{11.5cm}} \begin{tabular}{p{1.2cm}p{10.5cm}}
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} & The preconditioner data structure. Note that \emph{x}
must be chosen according to the real/complex, single/double must be chosen according to the real/complex, single/double
precision version of MLD2P4 under use.\\ precision version of MLD2P4 under use.\\
\verb|ptype| & \verb|character(len=*), intent(in)|.\\ \verb|ptype| & \verb|character(len=*), intent(in)|.\\
& The type of preconditioner. Its values are specified in Table~\ref{tab:precinit}.\\ & The type of preconditioner. Its values are specified in Table~\ref{tab:precinit}.\\
Note that the uppercase and lowercase letters can be used indifferently.\\
\verb|info| & \verb|integer, intent(out)|.\\ \verb|info| & \verb|integer, intent(out)|.\\
& Error code. See Section~\ref{sec:errors} for details.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\verb|nlev| & \verb|integer, optional, intent(in)|.\\ \verb|nlev| & \verb|integer, optional, intent(in)|.\\
& The number of levels of the multilevel preconditioner. & The number of levels of the multilevel preconditioner.
If \verb|nlev| is not present and \verb|ptype|='ML'/'ml', If \verb|nlev| is not present and \verb|ptype|=\verb|'ML'|, \verb|'ml'|,
then \verb|nlev|=2 is assumed. Otherwise, \verb|nlev| is ignored. then \verb|nlev|=2 is assumed. Otherwise, \verb|nlev| is ignored.\\
\end{tabular} \end{tabular}
@ -78,7 +81,7 @@ contained in \verb|val|.
\subsubsection*{Arguments} \subsubsection*{Arguments}
\begin{tabular}{p{1.2cm}p{11.5cm}} \begin{tabular}{p{1.2cm}p{10.5cm}}
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} must & The preconditioner data structure. Note that \emph{x} must
be chosen according to the real/complex, single/double precision be chosen according to the real/complex, single/double precision
@ -92,9 +95,13 @@ contained in \verb|val|.
\verb|intent(in)|.\\ \verb|intent(in)|.\\
& The value of the parameter to be set. The list of allowed & The value of the parameter to be set. The list of allowed
values and the corresponding data types is given in values and the corresponding data types is given in
Table~\ref{tab:params}.\\ Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
When the value is of type \verb|character(len=*)|,
uppercase and lowercase letters can be used indifferently.\\
\verb|info| & \verb|integer, intent(out)|.\\ \verb|info| & \verb|integer, intent(out)|.\\
& Error code. See Section~\ref{sec:errors} for details.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors}
for details.\\
%
%\verb|ilev| & \verb|integer, optional, intent(in)|.\\ %\verb|ilev| & \verb|integer, optional, intent(in)|.\\
% & For the multilevel preconditioner, the level at which the % & For the multilevel preconditioner, the level at which the
% preconditioner parameter has to be set. % preconditioner parameter has to be set.
@ -105,49 +112,50 @@ contained in \verb|val|.
\end{tabular} \end{tabular}
\ \\ \ \\
A variety of (one-level and multi-level) preconditioner can be obtained A variety of (one-level and multi-level) preconditioners can be obtained
by a suitable setting of the preconditioner parameters. These parameters by a suitable setting of the preconditioner parameters. These parameters
can be logically divided into four groups, i.e.\ parameters defining can be logically divided into four groups, i.e.\ parameters defining
\begin{enumerate} \begin{enumerate}
\item the type of multi-level preconditioner; \item the type of multi-level preconditioner;
\item the one-level preconditioner to be used as smoother; \item the one-level preconditioner used as smoother;
\item the aggregation algorithm; \item the aggregation algorithm;
\item the coarse-space correction at the coarsest level. \item the coarse-space correction at the coarsest level.
\end{enumerate} \end{enumerate}
A list of the parameters that can be set, along with their allowed and A list of the parameters that can be set, along with their allowed and
default values, is given in Tables~\ref{tab:p_type}-\ref{tab:p_coarse}. default values, is given in Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
For a better understanding of the meaning of the parameters, the user
is referred to Section \ref{sec:background}.
%
%Note that the routine allows to set different features of the %Note that the routine allows to set different features of the
%preconditioner at each level through the use of \verb|ilev|. %preconditioner at each level through the use of \verb|ilev|.
%This should be done by users with experience in the field of %This should be done by users with experience in the field of
%multi-level preconditioners. Non-expert users are recommended %multi-level preconditioners. Non-expert users are recommended
%to call \verb| mld_precset| without specifying \verb|ilev|. %to call \verb| mld_precset| without specifying \verb|ilev|.
\textbf{CORREGGERE LA ROUTINE E LA DOC INTERNA - ilev NON E' PIU'
ACCESSIBILE ALL'UTENTE.}
\begin{sidewaystable} \begin{sidewaystable}
\begin{center} \begin{center}
\begin{tabular}{|l|l|p{2cm}|l|p{7cm}|} \begin{tabular}{|l|l|p{2cm}|l|p{7cm}|}
\hline \hline
\verb|what| & \emph{data type} & \verb|val| & \emph{default} & \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\emph{comments} \\ \hline \textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{type of the multi-level preconditioner}}\\ \hline %\multicolumn{5}{|c|}{\emph{type of the multi-level preconditioner}}\\ \hline
\verb|mld_ml_type_| & \verb|character(len=*)| \verb|mld_ml_type_| & \verb|character(len=*)|
& 'ADD' \ \ \ 'MULT' & \texttt{'ADD'} \ \ \ \texttt{'MULT'}
& 'MULT' & \texttt{'MULT'}
& basic multi-level framework: additive or multiplicative & basic multi-level framework: additive or multiplicative
among the levels always additive inside a level) \\ among the levels (always additive inside a level) \\
\verb|mld_smoother_type_|& \verb|character(len=*)| \verb|mld_smoother_type_|& \verb|character(len=*)|
& 'DIAG' \ \ \ 'BJAC' \ \ \ 'AS' & \texttt{'DIAG'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'}
& 'AS' & \texttt{'AS'}
& basic one-level preconditioner (i.e.\ smoother) of the & basic one-level preconditioner (i.e.\ smoother) of the
multi-level preconditioner \\ multi-level preconditioner: diagonal, block Jacobi,
AS \\
\verb|mld_smoother_pos_| & \verb|character(len=*)| \verb|mld_smoother_pos_| & \verb|character(len=*)|
& 'PRE' \ \ \ 'POST' \ \ \ 'TWOSIDE' & \texttt{'PRE'} \ \ \ \texttt{'POST'} \ \ \ \texttt{'TWOSIDE'}
& 'POST' & \texttt{'POST'}
& ``position'' of the smoother: pre-smoother, post-smoother, & ``position'' of the smoother: pre-smoother, post-smoother,
pre-/post-smoother \\ pre- and post-smoother \\
\hline \hline
\end{tabular} \end{tabular}
\end{center} \end{center}
@ -157,72 +165,79 @@ ACCESSIBILE ALL'UTENTE.}
\begin{sidewaystable} \begin{sidewaystable}
\begin{center} \begin{center}
\begin{tabular}{|l|l|p{2cm}|l|p{7cm}|} \begin{tabular}{|l|l|p{2.6cm}|l|p{7cm}|}
\hline \hline
\verb|what| & \emph{data type} & \verb|val| & \emph{default} & \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\emph{comments} \\ \hline \textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{basic one-level preconditioner (smoother)}} \\ \hline %\multicolumn{5}{|c|}{\emph{basic one-level preconditioner (smoother)}} \\ \hline
\verb|mld_sub_ovr| & \verb|integer| \verb|mld_sub_ovr_| & \verb|integer|
& any number $\ge 0$ & any integer number $\ge 0$
& 1 & 1
& number of overlap in the basic Schwarz preconditioner \\ & Number of overlap layers. \\
\verb|mld_sub_restr_| & \verb|character(len=*)| \verb|mld_sub_restr_| & \verb|character(len=*)|
& 'HALO' \ \ \ 'NONE' & \texttt{'HALO'} \ \ \ \ \ \texttt{'NONE'}
& 'HALO' & \texttt{'HALO'}
& type of restriction operator used in basic Schwarz preconditioner: 'HALO' for taking into account contributions from the overlap \\ & Type of restriction operator:
\texttt{'HALO'} for taking into account the overlap, \texttt{'NONE'}
for neglecting it. \\
\verb|mld_sub_prol_| & \verb|character(len=*)| \verb|mld_sub_prol_| & \verb|character(len=*)|
& 'SUM' \ \ \ 'NONE' & \texttt{'SUM'} \ \ \ \ \ \texttt{'NONE'}
& 'NONE' & \texttt{'NONE'}
& type of prolongator operator used in basic Schwarz preconditioner: 'NONE' for neglecting contributions from the overlap \\ & Type of prolongator operator:
\texttt{'SUM'} for adding the contributions from the overlap, \texttt{'NONE'}
for neglecting them. \\
\verb|mld_sub_solve_| & \verb|character(len=*)| \verb|mld_sub_solve_| & \verb|character(len=*)|
& 'ILU' \ \ \ 'MILU' \ \ \ 'ILUT' \ \ \ 'UMF' \ \ \ 'SLU' & \texttt{'ILU'} \ \ \ \ \ \texttt{'MILU'} \ \ \ \ \ \texttt{'ILUT'} \ \ \ \ \
& 'UMF' \texttt{'UMF'} \ \ \ \ \ \texttt{'SLU'}
& available local solver: 'ILU' for incomplete LU, 'MILU' for modified incomplete LU, 'ILUT' & \texttt{'UMF'}
for incomplete LU with threshold, 'UMF' for complete LU using UMFPACK~\cite{UMFPACK} version 4.4, 'SLU' for complete LU using SuperLU~\cite{SUPERLU}, version 3.0 \\ & Local solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU,
plus triangular solve. \\
\verb|mld_sub_fillin_| & \verb|integer| \verb|mld_sub_fillin_| & \verb|integer|
& any number $\ge 0$ & any integer number $\ge 0$
& 0 & 0
& fill-in level for 'ILU', 'MILU' and 'ILUT' of local blocks\\ & Fill-in level $p$ of the incomplete LU factorizations. \\
\verb|mld_sub_thresh_| & \verb|real| \verb|mld_sub_thresh_| & \verb|real(|\emph{kind\_parameter}\verb|)|
& any number $\ge 0.$ & any real number $\ge 0$
& 0. & \texttt{0.e0} (or \texttt{0.d0})
& drop tolerance for 'ILUT' \\ & Drop tolerance $t$ in the ILU($p,t$) factorization. \\
\verb|mld_sub_ren_| & \verb|character(len=*)| \verb|mld_sub_ren_| & \verb|character(len=*)|
& 'RENUM\_NONE', 'RENUM\_GLOBAL' %, 'RENUM\_GPS' & \texttt{'RENUM\_NONE'}, \texttt{'RENUM\_GLOBAL'} %, \texttt{'RENUM_GPS'}
& & \texttt{'RENUM\_NONE'}
& reordering algorithm for the local blocks \\ & Row and column reordering of the local submatrices: no reordering,
reordering according to the global numbering of the rows and columns of
the whole matrix. \\
\hline \hline
\end{tabular} \end{tabular}
\end{center} \end{center}
\caption{Parameters defining the basic one-level preconditioner (smoother). \caption{Parameters defining the one-level preconditioner used as smoother.
\label{tab:p_smoother}} \label{tab:p_smoother}}
\end{sidewaystable} \end{sidewaystable}
\begin{sidewaystable} \begin{sidewaystable}
\begin{center} \begin{center}
\begin{tabular}{|l|l|p{2cm}|l|p{7cm}|} \begin{tabular}{|l|l|p{2.6cm}|l|p{7cm}|}
\hline \hline
\verb|what| & \emph{data type} & \verb|val| & \emph{default} & \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\emph{comments} \\ \hline \textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{aggregation algorithm}} \\ \hline %\multicolumn{5}{|c|}{\emph{aggregation algorithm}} \\ \hline
\verb|mld_aggr_alg_| & \verb|character(len=*)| \verb|mld_aggr_alg_| & \verb|character(len=*)|
& 'DEC' & \texttt{'DEC'}
& 'DEC' & \texttt{'DEC'}
& define the aggregation scheme. Now, only decoupled aggregation is available\\ & Aggregation algorithm. Currently, only the decoupled aggregation is available. \\
\verb|mld_aggr_kind_| & \verb|character(len=*)| \verb|mld_aggr_kind_| & \verb|character(len=*)|
& 'SMOOTH', 'RAW' & \texttt{'SMOOTH'} \ \ \ \ \ \texttt{'RAW'}
& 'SMOOTH' & \texttt{'SMOOTH'}
& define the type of aggregation technique (smoothed or nonsmoothed). \\ & Type of aggregation: smoothed or raw, i.e.\ using the tentative prolongator. \\
\verb|mld_aggr_thresh_| & \verb|real| \verb|mld_aggr_thresh_| & \verb|real(|\emph{kind\_parameter}\verb|)|
& any number $\in [0, 1]$ & any real number $\in [0, 1]$
& 0. & \texttt{0.e0} (or \texttt{0.d0})
& dropping threshold in aggregation \\ & The threshold $\theta$ in the aggregation algorithm. \\
\verb|mld_aggr_eig_| & \verb|character(len=*)| \verb|mld_aggr_eig_| & \verb|character(len=*)|
& 'A\_NORMI' & \texttt{'A\_NORMI'}
& & \texttt{'A\_NORMI'}
& define the algorithm to evaluate the maximum eigenvalue of $D^{-1}A$ for smoothed & Estimate of the maximum eigenvalue of $D^{-1}A$
aggregation. Currently only the infinity norm of the matrix A is available\\ for the smoothed aggregation. Currently, only the infinity norm of
the matrix is available. \\
\hline \hline
\end{tabular} \end{tabular}
\end{center} \end{center}
@ -232,36 +247,44 @@ aggregation. Currently only the infinity norm of the matrix A is available\\
\begin{sidewaystable} \begin{sidewaystable}
\begin{center} \begin{center}
\begin{tabular}{|l|l|p{2cm}|l|p{7cm}|} \begin{tabular}{|l|l|p{2.6cm}|l|p{7cm}|}
\hline \hline
\verb|what| & \emph{data type} & \verb|val| & \emph{default} & \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\emph{comments} \\ \hline \textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline %\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline
\verb|mld_coarse_mat_| & \verb|character(len=*)| \verb|mld_coarse_mat_| & \verb|character(len=*)|
& 'DISTR', 'REPL' & \texttt{'DISTR'} \ \ \ \ \ \texttt{'REPL'}
& 'DISTR' & \texttt{'DISTR'}
& Coarse matrix: distributed or replicated \\ & Coarsest matrix: distributed among the processors or replicated on each of them. \\
\verb|mld_coarse_solve_| & \verb|character(len=*)| \verb|mld_coarse_solve_| & \verb|character(len=*)|
& 'BJAC' \ \ \ 'UMF' \ \ \ 'SLU' \ \ \ 'SLUDIST' & \texttt{'BJAC'} \ \ \ \ \ \texttt{'UMF'} \ \ \ \ \ \ \ \ \texttt{'SLU'}
& 'BJAC' \ \ \ \ \ \texttt{'SLUDIST'}
& Only 'BJAC' and 'SLUDIST' can be used for distributed coarse matrix. 'BJAC' corresponds to some sweeps of a block-Jacobi solver, while 'SLUDIST' corresponds & \texttt{'BJAC'}
to the use of the external package SuperLU\_Dist~\cite{SUPERLUDIST}, version 2.0, for distributed sparse factorization and solve. \\ & Solver used at the coarsest level: block Jacobi, sequential LU from UMFPACK,
sequential LU from SuperLU, or distributed LU from SuperLU\_Dist.
If the coarsest matrix is distributed, only \texttt{'BJAC'} and \texttt{'SLUDIST'}
can be chosen; if it is replicated, only \emph{'BJAC'} or \texttt{'SLUDIST'} can
be selected. \\
\verb|mld_coarse_subsolve_| & \verb|character(len=*)| \verb|mld_coarse_subsolve_| & \verb|character(len=*)|
& 'ILU' \ \ \ 'MILU' \ \ \ 'ILUT' \ \ \ 'UMF' \ \ \ 'SLU' & \texttt{'ILU'} \ \ \ \ \ \ \ \texttt{'MILU'} \ \ \ \ \ \ \ \ \texttt{'ILUT'}
& 'UMF' \ \ \ \ \ \ \ \texttt{'UMF'} \ \ \ \ \ \ \ \texttt{'SLU'}
& available solver for diagonal local blocks of the coarse matrix, when 'BJAC' is used as coarse solver\\ & \texttt{'UMF'}
& Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver
is chosen as coarsest-level solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK,
LU from SuperLU, plus triangular solve. \\
\verb|mld_coarse_sweeps_|& \verb|integer| \verb|mld_coarse_sweeps_|& \verb|integer|
& any number $> 0$ & any integer number $> 0$
& 4 & \texttt{4}
& number of Block-Jacobi sweeps when 'BJAC' is used as coarse solver \\ & Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver. \\
\verb|mld_coarse_fillin_| & \verb|integer| \verb|mld_coarse_fillin_| & \verb|integer|
& any number $\ge 0$ & any integer number $\ge 0$
& 0 & \texttt{0}
& fill-in level in incomplete factorization of local diagonal blocks of the coarse matrix, when 'BJAC' is used as coarse solver and 'ILU' or 'MILU' is used as local solver \textbf{MODIFICA NOME PARAM. NEL SW} \\ & Fill-in level $p$ of the incomplete LU factorizations. \\
\verb|mld_coarse_thresh_| & \verb|real| \verb|mld_coarse_thresh_| & \verb|real(|\emph{kind\_parameter}\verb|)|
& any number $\ge 0.$ & any real number $\ge 0$
& 0. & \texttt{0.d0} (or \texttt{0.e0})
& drop tolerance in incomplete factorization of local diagonal blocks of the coarse matrix, when 'BJAC' is used as coarse solver and 'ILUT' is used as local solver \\ \hline & Drop tolerance $t$ in the ILU($p,t$) factorization. \\
\hline
\end{tabular} \end{tabular}
\end{center} \end{center}
\caption{Parameters defining the coarse-space correction at the coarsest \caption{Parameters defining the coarse-space correction at the coarsest
@ -282,20 +305,20 @@ the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
\subsubsection*{Arguments} \subsubsection*{Arguments}
\begin{tabular}{p{1.2cm}p{11.5cm}} \begin{tabular}{p{1.2cm}p{10.5cm}}
\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\ \verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
& The sparse matrix structure containing the local part of the & The sparse matrix structure containing the local part of the
matrix to be preconditioned. Note that \emph{x} must be chosen according matrix to be preconditioned. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use. to the real/complex, single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\ See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\ \verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
& The communication descriptor of a. See the PSBLAS User's Guide for & The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
details \cite{PSBLASGUIDE}.\\ details \cite{PSBLASGUIDE}.\\
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} must be chosen according & The preconditioner data structure. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.\\ to the real/complex, single/double precision version of MLD2P4 under use.\\
\verb|info| & \verb|integer, intent(out)|.\\ \verb|info| & \verb|integer, intent(out)|.\\
& Error code. See Section~\ref{sec:errors} for details.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\end{tabular} \end{tabular}
\clearpage \clearpage
@ -308,16 +331,16 @@ the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
\noindent \noindent
This routine computes $y = op(M^{-1})\, x$, where $M$ is a previously built This routine computes $y = op(M^{-1})\, x$, where $M$ is a previously built
preconditioner, stored in the \verb|p| data structure, and $op$ preconditioner, stored into \verb|p|, and $op$
denotes the preconditioner itself or its transpose, according to denotes the preconditioner itself or its transpose, according to
the value of \verb|trans|. the value of \verb|trans|.
Note that, when MLD2P4 is used with a Krylov solver from PSBLAS, Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
\verb|mld_precaply| is called within the PSBLAS routine \verb|mld_krylov| \verb|mld_precaply| is called within the PSBLAS routine \verb|mld_krylov|
and hence is completely transparent to the user. and hence it is completely transparent to the user.
\subsubsection*{Arguments} \subsubsection*{Arguments}
\begin{tabular}{p{1.2cm}p{11.5cm}} \begin{tabular}{p{1.2cm}p{10.5cm}}
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure, containing the local part of $M$. & The preconditioner data structure, containing the local part of $M$.
Note that \emph{x} must be chosen according Note that \emph{x} must be chosen according
@ -334,7 +357,7 @@ and hence is completely transparent to the user.
& The communication descriptor associated to the matrix to be & The communication descriptor associated to the matrix to be
preconditioned.\\ preconditioned.\\
\verb|info| & \verb|integer, intent(out)|.\\ \verb|info| & \verb|integer, intent(out)|.\\
& Error code. See Section~\ref{sec:errors} for details.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\verb|trans| & \verb|character(len=1), optional, intent(in).|\\ \verb|trans| & \verb|character(len=1), optional, intent(in).|\\
& If \verb|trans| = \verb|'N','n'| then $op(M^{-1}) = M^{-1}$; & If \verb|trans| = \verb|'N','n'| then $op(M^{-1}) = M^{-1}$;
if \verb|trans| = \verb|'T','t'| then $op(M^{-1}) = M^{-T}$ if \verb|trans| = \verb|'T','t'| then $op(M^{-1}) = M^{-T}$
@ -359,24 +382,24 @@ This routine deallocates the preconditioner data structure.
\subsubsection*{Arguments} \subsubsection*{Arguments}
\begin{tabular}{p{1.2cm}p{11.5cm}} \begin{tabular}{p{1.2cm}p{10.5cm}}
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} must be chosen according & The preconditioner data structure. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.\\ to the real/complex, single/double precision version of MLD2P4 under use.\\
\verb|info| & \verb|integer, intent(out)|.\\ \verb|info| & \verb|integer, intent(out)|.\\
& Error code. See Section~\ref{sec:errors} for details.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\end{tabular} \end{tabular}
\subsection{Subroutine mld\_precdescr\label{sec:precdescr}} \subsection{Subroutine mld\_precdescr\label{sec:precdescr}}
\begin{center} \begin{center}
\verb|mld_precdescr(p,iout)|\\ \verb|mld_precdescr(p,info,iout)|\\
\end{center} \end{center}
\noindent \noindent
This routine prints a description of the preconditioner This routine prints a description of the preconditioner
to a file. to the standard output or to a file.
\subsubsection*{Arguments} \subsubsection*{Arguments}
@ -384,9 +407,11 @@ to a file.
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(in)|.\\ \verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(in)|.\\
& The preconditioner data structure. Note that \emph{x} must be chosen according & The preconditioner data structure. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.\\ to the real/complex, single/double precision version of MLD2P4 under use.\\
\verb|info| & \verb|integer, intent(out)|.\\
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\verb|iout| & \verb|integer, intent(in), optional|.\\ \verb|iout| & \verb|integer, intent(in), optional|.\\
& The id of the file where the preconditioner description & The id of the file where the preconditioner description
will be printed, default is standard output.\\ will be printed; the default is the standard output.\\
\end{tabular} \end{tabular}
%%% Local Variables: %%% Local Variables:

@ -229,7 +229,10 @@ subroutine mld_cprecinit(p,ptype,info,nlev)
if (info /= 0) return if (info /= 0) return
p%baseprecv(ilev_)%iprcparm(:) = 0 p%baseprecv(ilev_)%iprcparm(:) = 0
p%baseprecv(ilev_)%rprcparm(:) = szero p%baseprecv(ilev_)%rprcparm(:) = szero
p%baseprecv(ilev_)%iprcparm(mld_coarse_solve_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_ p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0
@ -237,10 +240,8 @@ subroutine mld_cprecinit(p,ptype,info,nlev)
p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_ p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_
p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_ p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_
p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_ p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_ p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_
p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_ p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0
p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4 p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4
p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.e0/3.e0 p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.e0/3.e0

@ -244,6 +244,8 @@ subroutine mld_cprecseti(p,what,val,info,ilev)
select case (val) select case (val)
case(mld_umf_, mld_slu_) case(mld_umf_, mld_slu_)
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_
case(mld_bjac_)
p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
case default case default
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
end select end select

@ -229,7 +229,10 @@ subroutine mld_dprecinit(p,ptype,info,nlev)
if (info /= 0) return if (info /= 0) return
p%baseprecv(ilev_)%iprcparm(:) = 0 p%baseprecv(ilev_)%iprcparm(:) = 0
p%baseprecv(ilev_)%rprcparm(:) = dzero p%baseprecv(ilev_)%rprcparm(:) = dzero
p%baseprecv(ilev_)%iprcparm(mld_coarse_solve_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_ p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0
@ -237,10 +240,8 @@ subroutine mld_dprecinit(p,ptype,info,nlev)
p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_ p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_
p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_ p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_
p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_ p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_ p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_
p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_ p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0
p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4 p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4
p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.d0/3.d0 p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.d0/3.d0

@ -244,6 +244,8 @@ subroutine mld_dprecseti(p,what,val,info,ilev)
select case (val) select case (val)
case(mld_umf_, mld_slu_) case(mld_umf_, mld_slu_)
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_
case(mld_bjac_)
p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
case default case default
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
end select end select

@ -229,7 +229,10 @@ subroutine mld_sprecinit(p,ptype,info,nlev)
if (info /= 0) return if (info /= 0) return
p%baseprecv(ilev_)%iprcparm(:) = 0 p%baseprecv(ilev_)%iprcparm(:) = 0
p%baseprecv(ilev_)%rprcparm(:) = szero p%baseprecv(ilev_)%rprcparm(:) = szero
p%baseprecv(ilev_)%iprcparm(mld_coarse_solve_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_ p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0
@ -237,10 +240,8 @@ subroutine mld_sprecinit(p,ptype,info,nlev)
p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_ p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_
p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_ p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_
p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_ p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_ p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_
p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_ p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0
p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4 p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4
p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.e0/3.e0 p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.e0/3.e0

@ -244,6 +244,8 @@ subroutine mld_sprecseti(p,what,val,info,ilev)
select case (val) select case (val)
case(mld_umf_, mld_slu_) case(mld_umf_, mld_slu_)
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_
case(mld_bjac_)
p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
case default case default
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
end select end select

@ -229,7 +229,10 @@ subroutine mld_zprecinit(p,ptype,info,nlev)
if (info /= 0) return if (info /= 0) return
p%baseprecv(ilev_)%iprcparm(:) = 0 p%baseprecv(ilev_)%iprcparm(:) = 0
p%baseprecv(ilev_)%rprcparm(:) = dzero p%baseprecv(ilev_)%rprcparm(:) = dzero
p%baseprecv(ilev_)%iprcparm(mld_coarse_solve_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_ p%baseprecv(ilev_)%iprcparm(mld_smoother_type_) = mld_bjac_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_restr_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_ p%baseprecv(ilev_)%iprcparm(mld_sub_prol_) = psb_none_
p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_ren_) = 0
@ -237,10 +240,8 @@ subroutine mld_zprecinit(p,ptype,info,nlev)
p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_ p%baseprecv(ilev_)%iprcparm(mld_ml_type_) = mld_mult_ml_
p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_ p%baseprecv(ilev_)%iprcparm(mld_aggr_alg_) = mld_dec_aggr_
p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_ p%baseprecv(ilev_)%iprcparm(mld_aggr_kind_) = mld_smooth_prol_
p%baseprecv(ilev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_ p%baseprecv(ilev_)%iprcparm(mld_smoother_pos_) = mld_post_smooth_
p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_ p%baseprecv(ilev_)%iprcparm(mld_aggr_eig_) = mld_max_norm_
p%baseprecv(ilev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0 p%baseprecv(ilev_)%iprcparm(mld_sub_fillin_) = 0
p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4 p%baseprecv(ilev_)%iprcparm(mld_smoother_sweeps_) = 4
p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.d0/3.d0 p%baseprecv(ilev_)%rprcparm(mld_aggr_damp_) = 4.d0/3.d0

@ -244,6 +244,8 @@ subroutine mld_zprecseti(p,what,val,info,ilev)
select case (val) select case (val)
case(mld_umf_, mld_slu_) case(mld_umf_, mld_slu_)
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_
case(mld_bjac_)
p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = mld_ilu_n_
case default case default
p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_ p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_distr_mat_
end select end select

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