Nested alternating - triangular incomplete factorization methods

S. V. Gololobov, V. P. Il'in, A. M. Krylov, A. V. Petukhov

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We consider several versions of incomplete nested factorization methods for solving the large systems of linear algebraic equations (SLAEs) with sparse matrices which arise in grid approximations of the multi-dimensional boundary value problems. Our approach is based on the two-level iterative process in the Krylov subspaces in 3D case. Corresponding hierarchical incomplete factorization is applied to the block tridiagonal matrix structure. At the upper level, the diagonal blocks correspond to 2D grid subproblems which are factorized in the line-by-line framework. Instead of the low and upper triangular matrix factors, the alternating triangular matrices are used, which allows to apply the parallel counter sweeping approaches. The improvement of preconditioners is made by means of generalized compensation principles. To solve SLAE iterative conjugate direction methods in Krylov subspaces are applied. The efficiency of the proposed methods are demonstrated on the set of representative test problems.

Original languageEnglish
Article number012003
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 4 Jan 2021
EventInternational Conference on Marchuk Scientific Readings 2020, MSR 2020 - Akademgorodok, Novosibirsk, Russian Federation
Duration: 19 Oct 202023 Oct 2020


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