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Iterative solver for systems of linear equations with a sparse stiffness matrix on clusters

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Abstract

In this paper, a package of programs for solving systems of linear equations with a sparse matrix for computers with distributed memory is proposed. The package is based on an iterative algorithm for solving the initial system of equations with a preconditioner constructed using an algebraic domain decomposition. Such an approach makes it possible to simultaneously multiply the preconditioner and the stiffness matrix by a vector on a cluster. Also, to improve the efficiency of computation, the functionalities PARDISO and Sparse BLAS of the Intel®MKL library are used on each process. In addition to processes parallelization, the package uses OpenMP parallelization on each of these processes, as well as Intel®MKL internal functional parallelization.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    A. A. Kalinkin & Yu. M. Laevsky

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. A. Kalinkin & Yu. M. Laevsky

Authors
  1. A. A. Kalinkin
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  2. Yu. M. Laevsky
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Correspondence to A. A. Kalinkin.

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Original Russian Text © A.A. Kalinkin, Yu.M. Laevsky, 2012, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2012, Vol. 15, No. 2, pp. 223–228.

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Kalinkin, A.A., Laevsky, Y.M. Iterative solver for systems of linear equations with a sparse stiffness matrix on clusters. Numer. Analys. Appl. 5, 182–186 (2012). https://doi.org/10.1134/S1995423912020139

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  • DOI: https://doi.org/10.1134/S1995423912020139

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