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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 5, Pages 711–729 (Mi zvmmf10383)  

This article is cited in 4 scientific papers (total in 4 papers)

Combination of numerical and structured approaches to the construction of a second-order incomplete triangular factorization in parallel preconditioning methods

O. Yu. Milyukova

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

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.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 3


DOI: https://doi.org/10.7868/S0044466916050161

Full text: PDF file (313 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:5, 699–716

Bibliographic databases:

UDC: 519.61
Received: 05.06.2015
Revised: 06.10.2015

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  isi
    2. O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda sopryazhennykh gradientov s faktorizovannym predobuslovlivatelem”, Preprinty IPM im. M. V. Keldysha, 2020, 031, 22 pp.  mathnet  crossref
    3. O. Yu. Milyukova, “MPI+OpenMP realizatsiya metoda sopryazhennykh gradientov s predobuslovlivatelem blochnogo Yakobi IC1”, Preprinty IPM im. M. V. Keldysha, 2020, 083, 28 pp.  mathnet  crossref
    4. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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