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Num. Meth. Prog., 2019, Volume 20, Issue 4, Pages 516–527 (Mi vmp986)  

MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems

I. E. Kaporina, O. Yu. Milyukovab

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: A preconditioner for a large sparse nonsymmetric positive definite matrix is considered on the basis of its approximate inverse in the form of product of a lower triangular sparse matrix by an upper triangular matrix. For the class of matrices being considered, a new preconditioning based on the approximate block Jacobi with incomplete inverse LU-factorization preconditioning is proposed. For a parallel implementation of the corresponding preconditioned BiCGStab algorithm, the MPI+OpenMP techniques are used. The timing results obtained for the MPI+OpenMP and MPI implementations of the proposed preconditioning and for the Jacobi preconditioning used with the BiCGStab are compared using several test problems from the SuiteSparse collection (formerly known as the University of Florida sparse matrix collection).

Keywords: iterative solution of linear systems, sparse matrices, incomplete inverse triangular factorization, parallel preconditioning, BiCGStab method.

DOI: https://doi.org/10.26089/NumMet.v20r445

Full text: PDF file (564 kB)

UDC: 519.63
Received: 10.07.2019

Citation: I. E. Kaporin, O. Yu. Milyukova, “MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems”, Num. Meth. Prog., 20:4 (2019), 516–527

Citation in format AMSBIB
\Bibitem{KapMil19}
\by I.~E.~Kaporin, O.~Yu.~Milyukova
\paper MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems
\jour Num. Meth. Prog.
\yr 2019
\vol 20
\issue 4
\pages 516--527
\mathnet{http://mi.mathnet.ru/vmp986}
\crossref{https://doi.org/10.26089/NumMet.v20r445}


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