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Keldysh Institute preprints, 2014, 052, 32 pp. (Mi ipmp1904)  

This article is cited in 3 scientific papers (total in 3 papers)

Parallel version of the $2^\mathrm{nd}$ order incomplete triangular factorization preconditioned conjugate gradient method using special matrix reordering

O. Yu. Milyukova


Abstract: A parallel version of the stabilized $2^\mathrm{nd}$ order incomplete triangular factorization is considered for the use as a preconditioned for the conjugate gradient solution of linear algebraic systems with large sparse symmetric positive definite coefficient matrix. The reordering of the matrix is based on the use of certain domain decomposition type splitting which is further adjusted using a multi-level structure of separators. The incomplete factorization is organized using the truncation of fill-in by position at the separators and by value otherwise. Some theoretical results are given for the proposed method related, in particular, to its robustness. Numerical results are given obtained on the MVS-100K multiprocessor for the MPI implementation of the iterative linear solver.

Keywords: incomplete triangular factorization, parallel preconditioning, conjugate gradient linear solver.

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Citation: O. Yu. Milyukova, “Parallel version of the $2^\mathrm{nd}$ order incomplete triangular factorization preconditioned conjugate gradient method using special matrix reordering”, Keldysh Institute preprints, 2014, 052, 32 pp.

Citation in format AMSBIB
\Bibitem{Mil14}
\by O.~Yu.~Milyukova
\paper Parallel version of the $2^\mathrm{nd}$ order incomplete triangular factorization preconditioned conjugate gradient method using special matrix reordering
\jour Keldysh Institute preprints
\yr 2014
\papernumber 052
\totalpages 32
\mathnet{http://mi.mathnet.ru/ipmp1904}


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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, “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
    2. 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
    3. O. Yu. Milyukova, “Ob odnom parallelnom variante metoda nepolnogo treugolnogo razlozheniya vtorogo poryadka”, Matem. modelirovanie, 28:12 (2016), 107–121  mathnet  elib
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