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Keldysh Institute preprints, 2020, 083, 28 pp. (Mi ipmp2874)  

This article is cited in 2 scientific papers (total in 2 papers)

MPI+OpenMP parallel implementation of conjugate gradient method with the Block Jacobi preconditioner combined with IC1

O. Yu. Milyukova


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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-07-00841_а


DOI: https://doi.org/10.20948/prepr-2020-83

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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.

Citation in format AMSBIB
\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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s faktorizovannymi neyavnymi predobuslovlivatelyami”, Matem. modelirovanie, 33:10 (2021), 19–38  mathnet  crossref
    2. 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.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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