Geodesic
MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems
Numerical methods and programming, Tome 20 (2019) no. 4, pp. 516-527.

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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, incomplete inverse triangular factorization, parallel preconditioning, BiCGStab method.
Mots-clés : sparse matrices 
@article{VMP_2019_20_4_a14,
     author = {I. E. Kaporin and O. Yu. Milyukova},
     title = {MPI+OpenMP implementation of the {BiCGStab} method with explicit preconditioning for the numerical solution of sparse linear systems},
     journal = {Numerical methods and programming},
     pages = {516--527},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a14/}
}
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I. E. Kaporin; O. Yu. Milyukova. MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems. Numerical methods and programming, Tome 20 (2019) no. 4, pp. 516-527. http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a14/