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91 lines
6.0 KiB
TeX
91 lines
6.0 KiB
TeX
\section{General Overview\label{sec:overview}}
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\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}}
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{\textsc{\ref{sec:overview} General Overview}}
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The \textsc{Algebraic MultiGrid Preconditioners Package based on
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PSBLAS} (\textsc{AMG\-4\-PSBLAS}) provides parallel Algebraic MultiGrid (AMG) preconditioners (see, e.g., \cite{Briggs2000,Stuben_01}),
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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 symmetric positive definite (s.p.d) 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 preconditioners implemented in AMG4PSBLAS are obtained by combining
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3 different types of AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and a version of a Krylov-type cycle (K-cycle)~\cite{Briggs2000,Notay2008} are available, which can be combined with 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 smoothers. Also $\ell_1$ versions of Jacobi, block-Jacobi and Gauss-Seidel smoothers are available.
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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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two different coarsening strategies, based on aggregation, are available:
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\begin{itemize}
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\item a decoupled version of the well known smoothed aggregation procedure proposed in~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}, and already included in the previous versions of the package~\cite{BDDF2007,MLD2P4_TOMS};
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\item the first parallel implementation of a coupled version of Coarsening based on Compatible Weighted Matching introduced in~\cite{DV2013,DFV2018} and described in details in~\cite{DDF2020};
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\end{itemize}
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Either exact or approximate solvers can be used on the coarsest-level system. Specifically, different sparse LU factorizations from external
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packages, native incomplete LU and approximate inverse factorizations, weighted Jacobi, hybrid Gauss-Seidel, block-Jacobi solvers and recursive call to preconditioned Krylov methods are available. All the smoothers can be also exploited as one-level
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preconditioners.
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AMG4PSBLAS 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.
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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 AMG4PSBLAS 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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AMG4PSBLAS 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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kernels for sequential incomplete factorizations needed for the parallel block-Jacobi and additive Schwarz smoothers, and
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parallel Krylov solvers which can be used with the AMG4PSBLAS 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 AMG4PSBLAS, which was driven by the need to face the exascale challenge, has led to some important revisions and extentions of the PSBLAS infrastructure.
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The inter-process comunication required by AMG4PSBLAS is encapsulated
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in the PSBLAS routines;
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therefore, AMG4PSBLAS can be run on any parallel machine where PSBLAS
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implementations are available. In the most recent version of PSBLAS (release 3.7), a plug-in for GPU is included; it includes CUDA versions of
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main vector operations and of sparse matrix-vector multiplication, so that Krylov methods coupled with AMG4PBLAS preconditioners
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relying on Jacobi and block-Jacobi smoothers with sparse approximate inverses on the blocks can be efficiently executed on cluster of GPUs.
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AMG4PSBLAS 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 AMG4PSBLAS;
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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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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}. 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 AMG4PSBLAS 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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