Abstract:
Two non-iterative algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the Block Jacobi preconditioner combined with incomplete parameter-trimmed decomposition IC1. In Algorithm 1, the Domain Decomposition Ordering is used for the organization of OpenMP processing, OpenMP processing is used for almost all rows of the matrix. In Algorithm 2 uses sparsification of matrix structure, OpenMP processing is used for all rows of the matrix. 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 University of Florida collection test problems are presented.
Keywords:
iterative solution of linear systems, sparse matrices, incomplete
Cholesky factorization, parallel preconditioning, conjugate gradient method.
Citation:
O. Yu. Milyukova, “MPI+OpenMP parallel implementation of conjugate gradient method with the Block Jacobi preconditioner combined with IC1”, Keldysh Institute preprints, 2020, 083, 28 pp.
\Bibitem{Mil20}
\by O.~Yu.~Milyukova
\paper MPI+OpenMP parallel implementation of conjugate gradient method with the Block Jacobi preconditioner combined with IC1
\jour Keldysh Institute preprints
\yr 2020
\papernumber 083
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp2874}
\crossref{https://doi.org/10.20948/prepr-2020-83}
Linking options:
https://www.mathnet.ru/eng/ipmp2874
https://www.mathnet.ru/eng/ipmp/y2020/p83
This publication is cited in the following 6 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 predobuslovlivatelem IC(0) na osnove ispolzovaniya pereuporyadocheniya uzlov setki”, Preprinty IPM im. M. V. Keldysha, 2023, 035, 32 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.
O. Yu. Milyukova, “MPI+OpenMP parallel implementation of conjugate gradient method with factored implicit preconditioners”, Math. Models Comput. Simul., 14:3 (2022), 367–380
O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda sopryazhennykh gradientov c predobuslovlivatelem blochnogo nepolnogo obratnogo treugolnogo razlozheniya IC2S i IC1”, Preprinty IPM im. M. V. Keldysha, 2021, 048, 32 pp.
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