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80 lines
4.4 KiB
TeX
80 lines
4.4 KiB
TeX
\section{General Overview\label{sec:overview}}
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\markboth{\underline{MLD2P4 User's and Reference Guide}}
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{\underline{\ref{sec:overview} General Overview}}
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The \textsc{Multi-Level Domain Decomposition Parallel Preconditioners Package based on
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PSBLAS (MLD2P4}) provides \emph{multi-level Schwarz preconditioners}~\cite{dd2_96},
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to be used in the iterative solutions of sparse linear systems:
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\begin{equation}
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Ax=b,
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\label{system1}
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\end{equation}
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where $A$ is a square, real or complex, sparse matrix with a symmetric sparsity pattern.
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%
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%\textbf{NOTA: Caso non simmetrico, aggregazione con $(A+A^T)$ fatta!
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%Dovremmo implementare uno smoothed prolongator
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%adeguato e fare qualcosa di consistente anche con 1-lev Schwarz.}
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%
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These preconditioners have the following general features:
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\begin{itemize}
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\item both \emph{additive and hybrid multilevel} variants are implemented,
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i.e.\ variants that are additive among the levels and inside each level, and variants
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that are multiplicative among the levels and additive inside each level; the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level;
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\item a \emph{purely algebraic} approach is used to
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generate a sequence of coarse-level corrections to a basic AS preconditioner, without
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explicitly using any information on the geometry of the original problem (e.g.\ the
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discretization of a PDE). The \emph{smoothed aggregation} technique is applied
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as algebraic coarsening strategy~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}.
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\end{itemize}
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The package is written in \emph{Fortran~95}, following an
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\emph{object-oriented approach} through the exploitation of features
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such as abstract data type creation, functional
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overloading and dynamic memory management.% , while providing a smooth
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% path towards the integration in legacy application codes.
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% \textbf{NON MI PIACE QUESTO PERIODO, E' TROPPO LUNGO. RIUSCITE A SCRIVERLO MEGLIO?}
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The parallel implementation is based
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on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures.
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Single and double precision implementations of MLD2P4 are available for both the
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real and the complex case, that can be used through a single interface.
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MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
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in the context of the \emph{PSBLAS (Parallel Sparse BLAS)
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computational framework}~\cite{psblas_00}.
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PSBLAS is a library originally developed to address the parallel implementation of
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iterative solvers for sparse linear system, by providing basic linear algebra
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operators and data management facilities for distributed sparse matrices; it
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also includes parallel Krylov solvers, built on the top of the basic PSBLAS kernels.
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The preconditioners available in MLD2P4 can be used with these Krylov solvers.
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The choice of PSBLAS has been mainly motivated by the need of having
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a portable and efficient software infrastructure implementing ``de facto'' standard
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parallel sparse linear algebra kernels, to pursue goals such as performance,
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portability, modularity ed extensibility in the development of the preconditioner
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package. On the other hand, the implementation of MLD2P4 has led to some
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revisions and extentions of the PSBLAS kernels, leading to the
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recent PSBLAS 2.0 version~\cite{PSBLASGUIDE}. The inter-process comunication required
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by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
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MPI~\cite{MPI1} is explicitly called. Therefore, MLD2P4 can be run on any parallel
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machine where PSBLAS and MPI implementations are available.
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MLD2P4 has a layered and modular software architecture where three main layers can be identified.
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The lower layer consists of the PSBLAS kernels, the middle one implements
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the construction and application phases of the preconditioners, and the upper one
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provides a uniform and easy-to-use interface to all the preconditioners.
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This architecture allows for different levels of use of the package:
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few black-box routines at the upper layer allow non-expert users to easily
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build any preconditioner available in MLD2P4 and to apply it within a PSBLAS Krylov solver.
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On the other hand, the routines of the middle and lower layer can be used and extended
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by expert users to build new versions of multi-level Schwarz preconditioners.
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We provide here a description of the upper-layer routines, but not of the
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medium-layer ones.
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This guide is organized as follows: \textbf{ORGANIZZAZIONE DELLA GUIDA}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "userguide"
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%%% End:
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