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.
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.
\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}
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https://www.mathnet.ru/eng/ipmp2965
https://www.mathnet.ru/eng/ipmp/y2021/p48
This publication is cited in the following 3 articles:
O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s faktorizovannym predobuslovlivatelem na osnove ispolzovaniya pereuporyadocheniya uzlov setki”, Preprinty IPM im. M. V. Keldysha, 2023, 018, 29 pp.
O. Yu. Milyukova, “Sposoby MPI+OpenMP realizatsii metoda sopryazhennykh gradientov s predobuslovlivaniem blochnogo nepolnogo obratnogo treugolnogo razlozheniya IC1”, Preprinty IPM im. M. V. Keldysha, 2022, 002, 30 pp.
O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s predobuslovlivatelem IC(0) na osnove ispolzovaniya pereuporyadocheniya uzlov setki”, Preprinty IPM im. M. V. Keldysha, 2022, 063, 32 pp.
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