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One more iteration on the documentation. Also minor changes to precset.
This commit is contained in:
Salvatore Filippone
@@ -6,8 +6,12 @@ In this chapter are illustrated data structures used for definition of
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routines interfaces. This include data structure for sparse matrix,
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communication descriptor and preconditioner. These data structures are used for
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calling PSBLAS routines in Fortran~90 language and will be used to next
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chapters containing these callings. Their definitions are included in
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the modules \verb|psb_spmat_type|, \verb|psb_descriptor_type| and \verb|psb_prec_type|.
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chapters containing these callings.
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All the data types and subroutine interfaces are defined in the module
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\verb|psb_sparse_mod|; this will have to be included by every user
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subroutine that makes use of the library.
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\subsection{Descriptor data structure}
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+98
-4
@@ -22,7 +22,7 @@ subroutines. In this way, the library can take care of runtime memory
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requirements that are quite difficult or even impossible to predict at
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implementation or compilation time. The following presentation of the
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PSBLAS library follows the general structure of the proposal for
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serial Sparse BLAS~\cite{sblas97}, which in its turn is based on the
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serial Sparse BLAS~\cite{sblas97,sblas02}, which in its turn is based on the
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proposal for BLAS on dense matrices~\cite{BLAS1,BLAS2,BLAS3}.
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The applicability of sparse iterative solvers to many different areas
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@@ -63,7 +63,7 @@ the serial sparse BLAS, so that any extension made to the data
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structures of the serial kernels is available to the parallel
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version. The overall design and parallelization strategy have been
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influenced by the structure of the ScaLAPACK parallel
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library~\cite{scalapack}. The layered structure of the PSBLAS library
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library. The layered structure of the PSBLAS library
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is shown in figure~\ref{fig:psblas} ; lower layers of the library
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indicate an encapsulation relationship with upper layers. The ongoing
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discussion focuses on the Fortran~95 layer immediately below the
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@@ -76,7 +76,11 @@ that guarantees a portable and efficient communication layer. The
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Message Passing Interface code is encapsulated within the BLACS
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layer. However, in some cases, MPI routines are directly used either
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to improve efficiency or to implement communication patterns for which
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the BLACS package doesn't provide any method.
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the BLACS package doesn't provide any method.
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We assume that the user program has initialized a BLACS process grid
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with one column and as many rows as there are processes; the PSBLAS
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initialization routines will take the communication context for this
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grid and store internally for further use.
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\begin{figure}[h] \begin{center}
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\includegraphics[scale=0.45]{figures/psblas}
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@@ -87,7 +91,6 @@ the BLACS package doesn't provide any method.
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The PSBLAS library consists of two classes of subroutines that is, the
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{\em computational routines} and the {\em auxiliary routines}. The
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computational routine set includes:
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\begin{itemize}
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\item Sparse matrix by dense matrix product; \item Sparse triangular
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systems solution for block diagonal matrices;
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@@ -177,6 +180,97 @@ fetched from (neighbouring) processes. The descriptor of the index
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space is built exactly for the purpose of properly sequencing the
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communication steps required to achieve this objective.
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A simple application structure will walk through the index space
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allocation, matrix/vector creation and linear system solution as
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follows:
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\begin{enumerate}
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\item Initialize parallel environment with \verb|blacs_gridinit|
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\item Initialize index space with \verb|psb_cdall|
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\item Allocate sparse matrix and dense vectors with \verb|psb_spall|
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and \verb|psb_geall|
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\item Loop over all local rows, generate matrix and vector entries,
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and insert them with \verb|psb_spins| and \verb|psb_geins|
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\item Assemble the various entities:
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\begin{enumerate}
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\item \verb|psb_cdasb|
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\item \verb|psb_spasb|
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\item \verb|psb_geasb|
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\end{enumerate}
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\item Choose the preconditioner to be used with \verb|psb_precset| and
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build it with \verb|psb_precbld|
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\item Call the iterative method of choice, e.g. \verb|psb_bicgstab|
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\end{enumerate}
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This is the structure of the sample program
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\verb|test/pargen/ppde90.f90|.
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For a simulation in which the same discretization mesh is used over
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multiple time steps, the following structure may be more appropriate:
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\begin{enumerate}
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\item Initialize parallel environment with \verb|blacs_gridinit|
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\item Initialize index space with \verb|psb_cdall|
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\item Loop over the topology of the discretization mesh and build the
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descriptor with \verb|psb_cdins|
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\item Assemble the descriptor with \verb|psb_cdasb|
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\item Allocate the sparse matrices and dense vectors with
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\verb|psb_spall| and \verb|psb_geall|
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\item Loop over the time steps:
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\begin{enumerate}
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\item If after first time step,
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reinitialize the sparse matrix with \verb|psb_sprn|; also zero out
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the dense vectors;
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\item Loop over the mesh, generate the coefficients and insert/update
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them with \verb|psb_spins| and \verb|psb_geins|
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\item Assemble with \verb|psb_spasb| and \verb|psb_geasb|
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\item Choose and build preconditioner with \verb|psb_precset| and
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\verb|psb_precbld|
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\item Call the iterative method of choice, e.g. \verb|psb_bicgstab|
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\end{enumerate}
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\end{enumerate}
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The insertion routines will be called as many times as needed; it is
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clear that they only need be called on the data that is actually
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allocated to the current process, i.e. each process generates its own
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data.
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In principle there is no specific order in the calls to
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\verb|psb_spins|, nor is there a requirement to build a matrix row in
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its entirety before calling the routine; this allows the application
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programmer to walk through the discretization mesh element by element,
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generating the main part of a given matrix row but also contributions
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to the rows corresponding to neighbouring elements.
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From a functional point of view it is even possible to execute one
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call for each nonzero coefficient; however this would have a
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substantial computational overhead. It is therefore advisable to pack
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a certain amount of data into each call to the insertion routine, say
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touching on a few tens of rows; the best performng value would depend
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on both the architecture of the computer being used and on the problem
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structure.
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At the opposite extreme, it would be possible to generate the entire
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part of a coefficient matrix residing on a process and pass it in a
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single call to \verb|psb_spins|; this, however, would entail a
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doubling of memory occupation, and thus would be almost always far
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from optimal.
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\subsection{Programming model}
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The PSBLAS librarary is based on the Single Program Multiple Data
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(SPMD) programming model: each process participating in the
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computation performs the same actions on a chunk of data. Parallelism
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is thus data-driven.
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Because of this structure, practically all subroutines \emph{must} be
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called simultaneously by all processes participating in the
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computation, i.e each subroutine call acts implicitly as a
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synchronization point. The exceptions to this rule are:
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\begin{itemize}
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\item The insertion routines \verb|psb_cdins|, \verb|psb_spins| and
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\verb|psb_geins|;
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\item The error handling routines.
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\end{itemize}
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In particular, as per the discussion in the previous section, the
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insertion routines may be called a different number of times on each
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process, depending on the data distribution chosen by the user.
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "userguide"
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@@ -2,8 +2,7 @@
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\label{sec:methods}
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In this chapter we provide routines for preconditioners and iterative
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methods. Their
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interfaces are defined in the module \verb|psb_methd_mod|
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methods.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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+123
-29
@@ -18,38 +18,118 @@ many parameters that is possible to adjust to fit the user's needs:
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\subroutine{psb\_precset}{Sets the precodntioner type}
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\subroutine{psb\_precset}{Sets the preconditioner type}
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\syntax{call psb\_precset}{prec, ptype, iv, rs, rv, ierr}
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\syntax{call psb\_precset}{prec, ptype, iv, rs, ierr}
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\begin{description}
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\item[\bf On Entry]
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\item[prec]
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Scope: {\bf global} \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: e pronditioner data structure \precdata.
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Specified as: a pronditioner data structure \precdata.
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\item[ptype] the type of preconditioner.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Specified as: a string.
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Specified as: a character string, see usage notes.
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\item[iv] integer parameters for the precondtioner.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Specified as: an integer array.
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Specified as: an integer array, see usage notes.
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\item[rs]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\item[rv]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\item[ierr]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\end{description}
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Specified as: a long precision real number.
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\item[ierr]
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Scope: {\bf global} \\
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Type: {\bf required}\\
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\end{description}
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\section*{Usage Notes}
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The PSBLAS 2.0 contains a number of preconditioners, ranging from a
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simple diagonal scaling to 2-level domain decomposition. These
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preconditioners may use the SuperLU or the UMFPACK software, if
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installed; see~\cite{SUPERLU,UMFPACK}.
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Legal inputs to this subroutine are interpreted depending on the
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$ptype$ string as follows\footnote{The string is case-insensitive}:
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\begin{description}
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\item[NONE] No preconditioning, i.e. the preconditioner is just a copy
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operator.
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\item[DIAG] Diagonal scaling; each entry of the input vector is
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multiplied by the reciprocal of the sum of the absolute values of
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the coefficients in the corresponding row of matrix $A$;
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\item[ILU] Precondition by the incomplete LU factorization of the
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block-diagonal of matrix $A$, where block boundaries are determined
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by the data allocation boundaries for each process; requires no
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communication. Only $ILU(0)$ is currently implemented.
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\item[AS] Additive Schwarz preconditioner (see~\cite{PARA04}); in this
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case the user may specify additional flags through the integer
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vector \verb|ir| as follows:
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\begin{description}
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\item[$iv(1)$] Number of overlap levels, an integer $novr>0$, default
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$novr=1$.
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\item[$iv(2)$] Restriction operator, legal values: \verb|psb_halo_|,
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\verb|psb_none_|; default: \verb|psb_halo_|
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\item[$iv(3)$] Prolongation operator, legal values: \verb|psb_none_|,
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\verb|psb_sum_|, \verb|psb_avg_|, default: \verb|psb_none_|
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\item[$iv(4)$] Factorization type, legal values: \verb|f_ilu_n_|,
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\verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|.
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\end{description}
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Note that the default corresponds to a Restricted Additive Schwarz
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preconditioner with $ILU(0)$ and 1 level of overlap.
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\end{description}
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If a multilevel preconditioner is desired, the user should call
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\verb|psb_precset| once choosing AS, and a second time specifying
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$ptype=ML$ with the following optional parameters in $iv$ (see
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also~\cite{APNUM,DD2}):
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\begin{description}
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\item[$iv(1)$] Type of multilevel correction, legal values: \verb|no_ml_|,
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\verb|add_ml_prec_|, \verb|mult_ml_prec_|,
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default: \verb|mult_ml_prec_|;
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\item[$iv(2)$] Aggregation algorithm, legal values: \verb|loc_aggr_|;
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\item[$iv(3)$] Smoother type, legal values: \verb|no_smth_|,
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\verb|smth_omg_|, default: \verb|smth_omg_|;
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\item[$iv(4)$] Coarse matrix allocation, legal values:
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\verb|mat_distr_|, \verb|mat_repl_|, default: \verb|mat_distr_|
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\item[$iv(5)$] Smoother position, legal values: \verb|pre_smooth_|,
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\verb|post_smooth_|, \verb|smooth_both_|, default:
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\verb|post_smooth_|
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\item[$iv(6)$] Factorization type (for coarse matrix), legal values: \verb|f_ilu_n_|,
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\verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|;
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\item[$iv(7)$] Number of Jacobi sweeps for coarse system correction,
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default 1.
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\item[$rs$] Set the smoother parameter $\omega$ a user defined value;
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default: esitimate with the infinity norm of matrix $A$.
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\end{description}
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The 2-level preconditioners are based on the idea of building a
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coarse-space approximation $A_C$ of the matrix $A$; given a set $W_C$
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of coarse vertices, with size $n_C$, and a suitable restriction
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operator $R_C \in \Re^{n_C \times n}$, $A_C$ is defined as
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\[
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A_C=R_C A R_C^T .
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\]
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The prolongator $R_C^T$ is built with the smoothed aggregation technique,
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in which we start from a tentative prolongator that simply maps
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fine-level entries onto their aggregates $P_C$; if the user chooses
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\verb|no_smth_| this is the prolongator used, otherwise it is
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multiplied by a smoother \[ S = I - \omega D^{-1} A \], where $D$ is
|
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the diagonal of $A$ and $\omega$ may be imposed by the user or
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||||
estimated internally.
|
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The coarse space correction may be added to the fine level solution
|
||||
\verb|add_ml_prec_|
|
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\[
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M_{2L-A}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
|
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\]
|
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or it can be composed in a multiplicative framework as a pre-smoothed
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correction
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||||
\[
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M_{2L-H1}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1},
|
||||
\]
|
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post-smoothed correction
|
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\[
|
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M_{2L-H2}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}.
|
||||
\]
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or two-sided.
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||||
|
||||
|
||||
|
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@@ -60,11 +140,11 @@ Specified as: .
|
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\begin{description}
|
||||
\item[\bf On Entry]
|
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\item[a] the system sparse matrix.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a sparse matrix data structure \spdata.
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||||
\item[desc\_a] the problem communication descriptor.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a communication descriptor data structure \descdata.
|
||||
\item[upd]
|
||||
@@ -75,14 +155,14 @@ Specified as: a character.
|
||||
|
||||
\begin{description}
|
||||
\item[\bf On Return]
|
||||
\item[prec] the precodntioner.\\
|
||||
Scope: {\bf global} \\
|
||||
\item[prec] the preconditioner.\\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a precondtioner data structure \precdata\\
|
||||
\item[info] the return error code.\\
|
||||
Scope: {\bf local} \\
|
||||
Scope: {\bf global} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: an integer.\\
|
||||
Specified as: an integer, upon successful completion $info=0$ \\
|
||||
\end{description}
|
||||
|
||||
|
||||
@@ -95,15 +175,15 @@ Specified as: an integer.\\
|
||||
\begin{description}
|
||||
\item[\bf On Entry]
|
||||
\item[prec] the preconditioner.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a preconditioner data structure \precdata.
|
||||
\item[x] the source vector.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf require}\\
|
||||
Specified as: a double precision array.
|
||||
\item[desc\_a] the problem communication descriptor.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a communication data structure \descdata.
|
||||
\item[trans]
|
||||
@@ -119,13 +199,27 @@ Specified as: a double precision array.
|
||||
\begin{description}
|
||||
\item[\bf On Return]
|
||||
\item[y] the destination vector.
|
||||
Scope: {\bf global} \\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a double precision array.
|
||||
\item[info] the return error code.\\
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: an integer.\\
|
||||
Specified as: an integer, upon successful completion $info=0$ .\\
|
||||
\end{description}
|
||||
|
||||
|
||||
|
||||
\subroutine{psb\_prec\_descr}{Prints a description of current preconditioner}
|
||||
|
||||
\syntax{call psb\_prec\_descr}{prec}
|
||||
|
||||
\begin{description}
|
||||
\item[\bf On Entry]
|
||||
\item[prec] the preconditioner.
|
||||
Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: a preconditioner data structure \precdata.
|
||||
\end{description}
|
||||
|
||||
|
||||
|
||||
+67
-2
@@ -65,6 +65,11 @@ Type: {\bf required}\\
|
||||
Specified as: an integer variable.\\
|
||||
\end{description}
|
||||
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On exit from this routine the descriptor is in the build state
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
%
|
||||
%% psb_cdins %%
|
||||
@@ -108,6 +113,11 @@ Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
\end{description}
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item This routine may only be called if the descriptor is in the
|
||||
build state
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
@@ -134,6 +144,11 @@ Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
%\item[arg]
|
||||
\end{description}
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On exit from this routine the descriptor is in the assembled
|
||||
state.
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
@@ -285,6 +300,12 @@ Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
\end{description}
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On exit from this routine the sparse matrix is in the build
|
||||
state.
|
||||
\item The descriptor may be in either the build or assembled state.
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
@@ -342,6 +363,22 @@ Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
\end{description}
|
||||
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On entry to this routine the descriptor may be in either the
|
||||
build or assembled state.
|
||||
\item On entry to this routine the sparse matrix may be in either the
|
||||
build or update state.
|
||||
\item If the descriptor is in the build state, then the sparse matrix
|
||||
ought also be in the buld state; the action of the routine is to
|
||||
(implicitly) call \verb|psb_cdins| to add entries to the sparsity
|
||||
pattern;
|
||||
\item If the descriptor is in the assembled state, then any entries in
|
||||
the sparse matrix that would generate additional communication
|
||||
requirements will be ignored;
|
||||
\item If the matrix is in the update state, any entries in positions
|
||||
that were not present in the original matrix will be ignored.
|
||||
\end{enumerate}
|
||||
|
||||
%
|
||||
%% psb_spasb %%
|
||||
@@ -383,6 +420,22 @@ Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
\end{description}
|
||||
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On entry to this routine the descriptor must be in the
|
||||
assembled state, i.e. \verb|psb_cdasb| must already have been called.
|
||||
\item The sparse matrix may be in either the build or update state;
|
||||
\item Duplicate entries are detected and handled in both build and
|
||||
update state, with the exception of the error action that is only
|
||||
taken in the build state, i.e. on the first assembly;
|
||||
\item If the update choice is \verb|psb_upd_perm_|, then subsequent
|
||||
calls to \verb|psb_spins| to update the matrix must be arranged in
|
||||
such a way as to produce exactly the same sequence of coefficient
|
||||
values as encountered at the first assembly;
|
||||
\item On exit from this routine the matrix is in the assembled state,
|
||||
and thus is suitable for the computational routines.
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
|
||||
%% %
|
||||
@@ -474,7 +527,11 @@ Scope: {\bf local} \\
|
||||
Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
\end{description}
|
||||
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item On exit from this routine the sparse matrix is in the update
|
||||
state.
|
||||
\end{enumerate}
|
||||
%
|
||||
%% psb_spupdate %%
|
||||
%
|
||||
@@ -591,7 +648,7 @@ Specified as: a structured data of type \descdata.
|
||||
Scope: {\bf global}.\\
|
||||
Type: {\bf optional}.\\
|
||||
Specified as: integer, possible values: \verb|psb_dupl_ovwrt_|,
|
||||
\verb|psb_dupl_add_|, \verb|psb_dupl_err_|.
|
||||
\verb|psb_dupl_add_|.
|
||||
\end{description}
|
||||
|
||||
\begin{description}
|
||||
@@ -607,6 +664,14 @@ Type: {\bf required}\\
|
||||
Specified as: an integer variable.
|
||||
\end{description}
|
||||
|
||||
\section*{Notes}
|
||||
\begin{enumerate}
|
||||
\item Dense vectors/matrices do not have an associated state;
|
||||
\item Duplicate entries are either overwritten or added, there is no
|
||||
provision for raising an error condition.
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
%
|
||||
%% psb_asb %%
|
||||
%
|
||||
|
||||
@@ -91,6 +91,139 @@
|
||||
\include{methods}
|
||||
\include{precs}
|
||||
\include{error}
|
||||
|
||||
|
||||
\clearpage
|
||||
|
||||
\begin{thebibliography}{99}
|
||||
%
|
||||
\bibitem{BLAS1}
|
||||
Lawson, C., Hanson, R., Kincaid, D. and Krogh, F.,
|
||||
Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage,
|
||||
{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979.
|
||||
\bibitem{BLAS2}
|
||||
Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R.,
|
||||
An Extended Set of {F}ortran {B}asic {L}inear {A}lgebra {S}ubprograms,
|
||||
{ACM Trans. Math. Softw.} vol.~{14}, 1--17, 1988.
|
||||
\bibitem{BLAS3}
|
||||
Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I.,
|
||||
A Set of level 3 Basic Linear Algebra Subprograms,
|
||||
{ACM Trans. Math. Softw.} vol.~{16}, 1--17, 1990.
|
||||
\bibitem{DOUGLAS}
|
||||
R.E.~Bank and C.C.~Douglas,
|
||||
{\em SMMP: Sparse Matrix Multiplication Package},
|
||||
Advances in Computational Mathematics, 1993, 1, 127-137.
|
||||
(See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html})
|
||||
%
|
||||
\bibitem{PARA04FOREST}
|
||||
G.~Bella, S.~Filippone, A.~De Maio and M.~Testa,
|
||||
{\em A Simulation Model for Forest Fires},
|
||||
in J.~Dongarra, K.~Madsen, J.~Wasniewski, editors,
|
||||
Proceedings of PARA~04 Workshop on State of the Art
|
||||
in Scientific Computing, pp.~546--553, Lecture Notes in Computer Science,
|
||||
Springer, 2005.
|
||||
%
|
||||
\bibitem{PARA04}
|
||||
A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone,
|
||||
{\em Extending PSBLAS to Build Parallel Schwarz Preconditioners},
|
||||
in , J.~Dongarra, K.~Madsen, J.~Wasniewski, editors,
|
||||
Proceedings of PARA~04 Workshop on State of the Art
|
||||
in Scientific Computing, pp.~593--602, Lecture Notes in Computer Science,
|
||||
Springer, 2005.
|
||||
%
|
||||
\bibitem{CAI_SAAD}
|
||||
X.~C.~Cai and Y.~Saad,
|
||||
{\em Overlapping Domain Decomposition Algorithms for General Sparse Matrices},
|
||||
Numerical Linear Algebra with Applications, 3(3), pp.~221--237, 1996.
|
||||
%
|
||||
\bibitem{CAI_SARKIS}
|
||||
X.C.~Cai and M.~Sarkis,
|
||||
{\em A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems},
|
||||
SIAM Journal on Scientific Computing, 21(2), pp.~792--797, 1999.
|
||||
%
|
||||
\bibitem{CAI_WIDLUND}
|
||||
X.C.~Cai and O.~B.~Widlund,
|
||||
{\em Domain Decomposition Algorithms for Indefinite Elliptic Problems},
|
||||
SIAM Journal on Scientific and Statistical Computing, 13(1), pp.~243--258, 1992.
|
||||
%
|
||||
\bibitem{DD1}
|
||||
T.~Chan and T.~Mathew,
|
||||
{\em Domain Decomposition Algorithms},
|
||||
in A.~Iserles, editor, Acta Numerica 1994, pp.~61--143, 1994.
|
||||
Cambridge University Press.
|
||||
%
|
||||
\bibitem{APNUM06}
|
||||
P.~D'Ambra, D.~di Serafino and S.~Filippone,
|
||||
On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners,
|
||||
Applied Numerical Mathematics, to appear, 2006.
|
||||
%
|
||||
\bibitem{UMFPACK}
|
||||
T.A.~Davis,
|
||||
{\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
|
||||
Method with a Column Pre-ordering Strategy},
|
||||
ACM Transactions on Mathematical Software, 30, pp.~196--199, 2004.
|
||||
(See also {\tt http://www.cise.ufl.edu/~davis/})
|
||||
%
|
||||
\bibitem{SUPERLU}
|
||||
J.W.~Demmel, S.C.~Eisenstat, J.R.~Gilbert, X.S.~Li and J.W.H.~Liu,
|
||||
A supernodal approach to sparse partial pivoting,
|
||||
SIAM Journal on Matrix Analysis and Applications, 20(3), pp.~720--755, 1999.
|
||||
%
|
||||
\bibitem{BLACS}
|
||||
J.~J.~Dongarra and R.~C.~Whaley,
|
||||
{\em A User's Guide to the BLACS v.~1.1},
|
||||
Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of
|
||||
Tennessee, March 1995 (updated May 1997).
|
||||
%
|
||||
\bibitem{sblas97}
|
||||
I.~Duff, M.~Marrone, G.~Radicati and C.~Vittoli,
|
||||
{\em Level 3 Basic Linear Algebra Subprograms for Sparse Matrices:
|
||||
a User Level Interface},
|
||||
ACM Transactions on Mathematical Software, 23(3), pp.~379--401, 1997.
|
||||
%
|
||||
\bibitem{sblas02}
|
||||
I.~Duff, M.~Heroux and R.~Pozo,
|
||||
{\em An Overview of the Sparse Basic Linear
|
||||
Algebra Subprograms: the New Standard from the BLAS Technical Forum},
|
||||
ACM Transactions on Mathematical Software, 28(2), pp.~239--267, 2002.
|
||||
\bibitem{PSBLAS}
|
||||
S.~Filippone and M.~Colajanni,
|
||||
{\em PSBLAS: A Library for Parallel Linear Algebra
|
||||
Computation on Sparse Matrices},
|
||||
\newblock
|
||||
ACM Transactions on Mathematical Software, 26(4), pp.~527--550, 2000.
|
||||
%
|
||||
\bibitem{KIVA3PSBLAS}
|
||||
S.~Filippone, P.~D'Ambra, M.~Colajanni,
|
||||
{\em Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics
|
||||
Applications Code on Linux Clusters},
|
||||
in G.~Joubert, A.~Murli, F.~Peters, M.~Vanneschi, editors,
|
||||
Parallel Computing - Advances \& Current Issues,
|
||||
pp.~441--448, Imperial College Press, 2002.
|
||||
%
|
||||
\bibitem{machiels}
|
||||
{Machiels, L. and Deville, M.}
|
||||
{\em Fortran 90: An entry to object-oriented programming for the solution
|
||||
of partial differential equations.}
|
||||
{ACM Trans. Math. Softw.} vol.~{23}, 32--49.
|
||||
\bibitem{metcalf}
|
||||
{Metcalf, M., Reid, J. and Cohen, M.}
|
||||
{\em Fortran 95/2003 explained.}
|
||||
{Oxford University Press}, 2004.
|
||||
%
|
||||
\bibitem{DD2}
|
||||
B.~Smith, P.~Bjorstad and W.~Gropp,
|
||||
{\em Domain Decomposition: Parallel Multilevel Methods for Elliptic
|
||||
Partial Differential Equations},
|
||||
Cambridge University Press, 1996.
|
||||
%
|
||||
\bibitem{MPI1}
|
||||
M.~Snir, S.~Otto, S.~Huss-Lederman, D.~Walker and J.~Dongarra,
|
||||
{\em MPI: The Complete Reference. Volume 1 - The MPI Core}, second edition,
|
||||
MIT Press, 1998.
|
||||
%
|
||||
\end{thebibliography}
|
||||
|
||||
\end{document}
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
|
||||
+19084
-16662
File diff suppressed because one or more lines are too long
@@ -158,7 +158,8 @@ module psb_prec_type
|
||||
end interface
|
||||
|
||||
interface psb_prec_descr
|
||||
module procedure psb_file_prec_descr, psb_zfile_prec_descr
|
||||
module procedure psb_out_prec_descr, psb_file_prec_descr, &
|
||||
& psb_zout_prec_descr, psb_zfile_prec_descr
|
||||
end interface
|
||||
|
||||
interface psb_prec_short_descr
|
||||
@@ -167,6 +168,16 @@ module psb_prec_type
|
||||
|
||||
contains
|
||||
|
||||
subroutine psb_out_prec_descr(p)
|
||||
type(psb_dprec_type), intent(in) :: p
|
||||
call psb_file_prec_descr(6,p)
|
||||
end subroutine psb_out_prec_descr
|
||||
|
||||
subroutine psb_zout_prec_descr(p)
|
||||
type(psb_zprec_type), intent(in) :: p
|
||||
call psb_zfile_prec_descr(6,p)
|
||||
end subroutine psb_zout_prec_descr
|
||||
|
||||
subroutine psb_file_prec_descr(iout,p)
|
||||
integer, intent(in) :: iout
|
||||
type(psb_dprec_type), intent(in) :: p
|
||||
|
||||
@@ -179,10 +179,8 @@ subroutine psb_dprecset(p,ptype,iv,rs,rv,info)
|
||||
if (isz >= 3) p%baseprecv(2)%iprcparm(smth_kind_) = iv(3)
|
||||
if (isz >= 4) p%baseprecv(2)%iprcparm(coarse_mat_) = iv(4)
|
||||
if (isz >= 5) p%baseprecv(2)%iprcparm(smth_pos_) = iv(5)
|
||||
if (isz >= 6) p%baseprecv(2)%iprcparm(glb_smth_) = iv(6)
|
||||
if (isz >= 7) p%baseprecv(2)%iprcparm(f_type_) = iv(7)
|
||||
if (isz >= 8) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(8)
|
||||
|
||||
if (isz >= 6) p%baseprecv(2)%iprcparm(f_type_) = iv(6)
|
||||
if (isz >= 7) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(7)
|
||||
end if
|
||||
|
||||
if (present(rs)) then
|
||||
|
||||
@@ -179,9 +179,8 @@ subroutine psb_zprecset(p,ptype,iv,rs,rv,info)
|
||||
if (isz >= 3) p%baseprecv(2)%iprcparm(smth_kind_) = iv(3)
|
||||
if (isz >= 4) p%baseprecv(2)%iprcparm(coarse_mat_) = iv(4)
|
||||
if (isz >= 5) p%baseprecv(2)%iprcparm(smth_pos_) = iv(5)
|
||||
if (isz >= 6) p%baseprecv(2)%iprcparm(glb_smth_) = iv(6)
|
||||
if (isz >= 7) p%baseprecv(2)%iprcparm(f_type_) = iv(7)
|
||||
if (isz >= 8) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(8)
|
||||
if (isz >= 6) p%baseprecv(2)%iprcparm(f_type_) = iv(6)
|
||||
if (isz >= 7) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(7)
|
||||
|
||||
end if
|
||||
|
||||
|
||||
@@ -251,11 +251,11 @@ program df_sample
|
||||
case(7)
|
||||
call psb_precset(pre,'asm',iv=(/ml,halo_,none_/))
|
||||
call psb_precset(pre,'ml',&
|
||||
& iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,1,f_ilu_n_,4/))
|
||||
& iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,f_ilu_n_,4/))
|
||||
case(8)
|
||||
call psb_precset(pre,'asm',iv=(/ml,halo_,none_/))
|
||||
call psb_precset(pre,'ml',&
|
||||
& iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,1,f_umf_,4/))
|
||||
& iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,f_umf_,4/))
|
||||
|
||||
case default
|
||||
call psb_precset(pre,'ilu')
|
||||
|
||||
@@ -173,19 +173,6 @@ program pde90
|
||||
call psb_precset(pre,'asm',iv=(/novr,halo_,none_/))
|
||||
case(rash_)
|
||||
call psb_precset(pre,'asm',iv=(/novr,nohalo_,none_/))
|
||||
case(ras2lv_)
|
||||
ptype='asm'
|
||||
call psb_precset(pre,ptype,iv=(/novr,halo_,none_/))
|
||||
ptype='ml'
|
||||
call psb_precset(pre,ptype,&
|
||||
&iv=(/add_ml_prec_,loc_aggr_,no_smth_,mat_repl_,&
|
||||
& pre_smooth_/),rs=0.d0)
|
||||
case(ras2lvm_)
|
||||
ptype='asm'
|
||||
call psb_precset(pre,ptype,iv=(/novr,halo_,none_/))
|
||||
ptype='ml'
|
||||
call psb_precset(pre,ptype,&
|
||||
& iv=(/mult_ml_prec_,glb_aggr_,pre_smooth_/),rs=0.d0)
|
||||
end select
|
||||
|
||||
call blacs_barrier(icontxt,'ALL')
|
||||
|
||||
Reference in New Issue
Block a user