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 Keldysh Institute preprints, 2021, 048, 32 pp. (Mi ipmp2965)

MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1

O. Yu. Milyukova

Abstract: The paper proposes a new preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix by the method of conjugate gradients – Block Incomplete Inverse Cholesky BIIC preconditioner in combination with a triangular first-order decomposition 'by value' - BIIC-IC1. The algorithm based on MPI+OpenMP techniques is proposed for the construction and application of the BIIC preconditioner combined with stabilized triangular decomposition of the second order 'by value' (BIIC-IS2S). In this case, the BIIC-IC2S preconditioner uses the number of blocks multiple of the number of processors used and the number of threads used. Two algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the BIIC-IC1 preconditioner. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.

Keywords: sparse matrices, implicit block preconditioning, incomplete Cholesky factorization, parallel preconditioning, conjugate gradient method.

DOI: https://doi.org/10.20948/prepr-2021-48

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Citation: O. Yu. Milyukova, “MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1”, Keldysh Institute preprints, 2021, 048, 32 pp.

Citation in format AMSBIB
\Bibitem{Mil21} \by O.~Yu.~Milyukova \paper MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1 \jour Keldysh Institute preprints \yr 2021 \papernumber 048 \totalpages 32 \mathnet{http://mi.mathnet.ru/ipmp2965} \crossref{https://doi.org/10.20948/prepr-2021-48}