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106 lines
6.1 KiB
TeX
106 lines
6.1 KiB
TeX
\section{General Overview\label{sec:overview}}
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\markboth{\textsc{MLD2P4 User's and Reference Guide}}
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{\textsc{\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 parallel Algebraic MultiGrid (AMG) and Domain
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Decomposition preconditioners (see, e.g., \cite{Briggs2000,Stuben_01,dd2_96}),
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to be used in the iterative solution of 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.
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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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The name of the package comes from its original implementation, containing
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multi-level additive and hybrid Schwarz preconditioners, as well as one-level additive
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Schwarz preconditioners. The current version extends the original plan by including
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multi-level cycles and smoothers widely used in multigrid methods.
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The multi-level preconditioners implemented in MLD2P4 are obtained by combining
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AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and
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K-cycles~\cite{Briggs2000,Notay2008} are available, which allow to define
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almost all the preconditioners in the package, including the multi-level hybrid
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Schwarz ones; a specific cycle is implemented to obtain multi-level additive
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Schwarz preconditioners. The Jacobi, hybrid
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%\footnote{see Note 2 in Table~\ref{tab:p_coarse}, p.~28.}
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forward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods
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are available as smoothers. An algebraic approach is used to generate a hierarchy of
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coarse-level matrices and operators, without explicitly using any information on the
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geometry of the original problem, e.g., the discretization of a PDE. To this end,
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the smoothed aggregation technique~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}
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is applied. Either exact or approximate solvers can be used on the coarsest-level
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system. Specifically, different sparse LU factorizations from external
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packages, and native incomplete LU factorizations and Jacobi, hybrid Gauss-Seidel,
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and block-Jacobi solvers are available. All smoothers can be also exploited as one-level
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preconditioners.
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MLD2P4 is written in Fortran~2003, following an
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object-oriented design through the exploitation of features
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such as abstract data type creation, type extension, functional overloading, and
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dynamic memory management. % \textbf{Va bene cos\'{i} o \`e meglio
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% fare riferimento alle classi?}
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The parallel implementation is based on a Single Program Multiple Data
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(SPMD) paradigm. Single and
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double precision implementations of MLD2P4 are available for both the
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real and the complex case, which can be used through a single
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interface.
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MLD2P4 has been designed to implement scalable and easy-to-use
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multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS)
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computational framework~\cite{psblas_00,PSBLAS3}. PSBLAS provides basic linear algebra
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operators and data management facilities for distributed sparse matrices,
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as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners.
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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 original PSBLAS kernels.
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The inter-process comunication required by MLD2P4 is encapsulated
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in the PSBLAS routines;
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% , except few cases where MPI~\cite{MPI1} is explicitly called.
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therefore, MLD2P4 can be run on any parallel machine where PSBLAS
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implementations are available.
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MLD2P4 has a layered and modular software architecture where three main layers can be
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identified. 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 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 all users to easily
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build and apply any preconditioner available in MLD2P4;
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facilities are also available allowing expert users to extend the set of smoothers
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and solvers for building new versions of the preconditioners (see
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Section~\ref{sec:adding}).
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We note that the user interface of MLD2P4 2.1 has been extended with respect to the
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previous versions in order to separate the construction of the multi-level hierarchy from
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the construction of the smoothers and solvers, and to allow for more flexibility
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at each level. The software architecture described in~\cite{MLD2P4_TOMS} has significantly
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evolved too, in order to fully exploit the Fortran~2003 features implemented in PSBLAS 3.
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However, compatibility with previous versions has been preserved.
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This guide is organized as follows. General information on the distribution of the source
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code is reported in Section~\ref{sec:distribution}, while details on the configuration
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and installation of the package are given in Section~\ref{sec:building}. A short description
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of the preconditioners implemented in MLD2P4 is provided in Section~\ref{sec:background},
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to help the users in choosing among them. The basics for building and applying the
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preconditioners with the Krylov solvers implemented in PSBLAS are reported
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in~Section~\ref{sec:started}, where the Fortran codes of a few sample programs
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are also shown. A reference guide for the user interface routines is provided
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in Section~\ref{sec:userinterface}. Information on the extension of the package
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through the addition of new smoothers and solvers is reported in Section~\ref{sec:adding}.
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The error handling mechanism used by the package
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is briefly described in Section~\ref{sec:errors}. The copyright terms concerning the
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distribution and modification of MLD2P4 are reported in Appendix~\ref{sec:license}.
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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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