About one parallel version of the $2^{\text{nd}}$ order incomplete triangular factorization

O. Yu. Milyukova

Keldysh Institute of Applied Mathematics of Rus. Acad. Sci., Moscow

Abstract: One parallel version of the stabilized $2^{\text{nd}}$ order incomplete triangular factorization is considered as preconditioner for the conjugate gradient method. This parallel version is based on the reordering of the matrix used of certain domain decomposition type splitting with separators. The incomplete factorization is organized using the truncation of fill-in “by value” within the subdomains and “by position” and “by value” at the separators. Non-failure operation of the considered method is theoretically proved, non-failure operation and convergence speed of the parallel method are numerically investigated. For an MPI implementation of the iterative linear solver, numerical results are given obtained for matrices from the University of Florida collection.

Keywords: iterative linear solvers, sparse matrices, incomplete triangular factorization, parallel preconditioning.

Received: 06.10.2015

 English version: Mathematical Models and Computer Simulations, 2019, 11:2, 309–320

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