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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 1096–1113 (Mi zvmmf461)  

This article is cited in 8 scientific papers (total in 8 papers)

Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids

O. Yu. Milyukova

Institute for Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

Abstract: Parallel analogs of the variants of the incomplete Cholesky-conjugate gradient method and the modified incomplete Cholesky-conjugate gradient method for solving elliptic equations on uniform triangular and unstructured triangular grids on parallel computer systems with the MIMD architecture are considered. The construction of parallel methods is based on the use of various variants of ordering the grid points depending on the decomposition of the computation domain. Results of the theoretic and experimental studies of the convergence rate of these methods are presented. The solution of model problems on a moderate number processors is used to examine the efficiency of the proposed parallel methods.

Key words: parallel iterative methods, systems of linear algebraic equations, elliptic boundary value problems, finite difference method.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 1044–1060

Bibliographic databases:

UDC: 519.632.4
Received: 08.02.2005
Revised: 30.01.2006

Citation: O. Yu. Milyukova, “Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1096–1113; Comput. Math. Math. Phys., 46:6 (2006), 1044–1060

Citation in format AMSBIB
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\by O.~Yu.~Milyukova
\paper Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 1096--1113
\mathnet{http://mi.mathnet.ru/zvmmf461}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285367}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 1044--1060
\crossref{https://doi.org/10.1134/S096554250606011X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746105649}


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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. I. E. Kaporin, O. Yu. Milyukova, “Optimizatsiya faktorizovannykh predobuslovlivanii metoda sopryazhennykh gradientov dlya resheniya sistem lineinykh algebraicheskikh uravnenii s simmetrichnoi polozhitelno opredelennoi matritsei”, Preprinty IPM im. M. V. Keldysha, 2013, 013, 17 pp.  mathnet
    2. O. Yu. Milyukova, “Parallelnye varianty metoda nepolnogo treugolnogo razlozheniya vtorogo poryadka sopryazhennykh gradientov na osnove ispolzovaniya spetsialnogo pereuporyadocheniya matritsy koeffitsientov”, Preprinty IPM im. M. V. Keldysha, 2014, 052, 32 pp.  mathnet
    3. O. Yu. Milyukova, “Sochetanie chislovykh i strukturnykh podkhodov k postroeniyu nepolnogo treugolnogo razlozheniya vtorogo poryadka v parallelnykh algoritmakh predobuslovlennogo metoda sopryazhennykh gradientov”, Preprinty IPM im. M. V. Keldysha, 2015, 010, 32 pp.  mathnet
    4. O. Yu. Milyukova, “Combination of numerical and structured approaches to the construction of a second-order incomplete triangular factorization in parallel preconditioning methods”, Comput. Math. Math. Phys., 56:5 (2016), 699–716  mathnet  crossref  crossref  isi  elib
    5. O. Yu. Milyukova, “Ob odnom parallelnom variante metoda nepolnogo treugolnogo razlozheniya vtorogo poryadka”, Matem. modelirovanie, 28:12 (2016), 107–121  mathnet  elib
    6. 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
    7. O. Yu. Milyukova, “MPI+OpenMPI realizatsiya metoda sopryazhennykh gradientov s faktorizovannym predobuslovlivatelem”, Preprinty IPM im. M. V. Keldysha, 2020, 031, 22 pp.  mathnet  crossref
    8. 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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