This article is cited in 11 scientific papers (total in 11 papers)
Combination of numerical and structured approaches to the construction of a second-order incomplete triangular factorization in parallel preconditioning methods
Abstract:
Parallel versions of the stabilized second-order incomplete triangular factorization conjugate gradient method in which the reordering of the coefficient matrix corresponding to the ordering based on splitting into subdomains with separators are considered. The incomplete triangular factorization is organized using the truncation of fill-in “by value” at internal nodes of subdomains, and “by value” and “by positions” on the separators. This approach is generalized for the case of constructing a parallel version of preconditioning the second-order incomplete LU factorization for nonsymmetric diagonally dominant matrices with. The reliability and convergence rate of the proposed parallel methods is analyzed. The proposed algorithms are implemented using MPI, results of solving benchmark problems with matrices from the collection of the University of Florida are presented.
Key words:
iterative solution of systems of linear algebraic equations, sparse matrices, incomplete triangular factorization, parallel preconditioning.
Citation:
O. Yu. Milyukova, “Combination of numerical and structured approaches to the construction of a second-order incomplete triangular factorization in parallel preconditioning methods”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 711–729; Comput. Math. Math. Phys., 56:5 (2016), 699–716
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Linking options:
https://www.mathnet.ru/eng/zvmmf10383
https://www.mathnet.ru/eng/zvmmf/v56/i5/p711
This publication is cited in the following 11 articles:
O. Yu. Milyukova, “Some ways of parallel implementation of the conjugate gradient method with an implicit factorized preconditioner”, Math. Models Comput. Simul., 16:4 (2024), 638–653
O. Yu. Milyukova, “Sochetanie chislovykh i strukturnykh podkhodov v parallelnom metode predobuslovlivaniya nepolnogo treugolnogo razlozheniya pervogo poryadka”, Preprinty IPM im. M. V. Keldysha, 2024, 075, 28 pp.
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, “Parallelnaya realizatsiya metoda sopryazhennykh gradientov s predobuslovlivatelem IC1 na osnove ispolzovaniya pereuporyadocheniya uzlov setki”, Preprinty IPM im. M. V. Keldysha, 2023, 061, 28 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+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.
O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda sopryazhennykh gradientov s faktorizovannym predobuslovlivatelem”, Preprinty IPM im. M. V. Keldysha, 2020, 031, 22 pp.
O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s predobuslovlivatelem blochnogo Yakobi IC1”, Preprinty IPM im. M. V. Keldysha, 2020, 083, 28 pp.
S. L. Gonzaga de Oliveira, J. A. B. Bernardes, G. O. Chagas, “An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method”, Comput. Appl. Math., 37:3 (2018), 2965–3004
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