TY - JOUR

T1 - Nested alternating - triangular incomplete factorization methods

AU - Gololobov, S. V.

AU - Il'in, V. P.

AU - Krylov, A. M.

AU - Petukhov, A. V.

N1 - Funding Information: The work is supported by RFBR grant N18-01-00295 in theoretical part an RSF grant N19-11-00048 in computational experiments part. Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/4

Y1 - 2021/1/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85100724932&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1715/1/012003

DO - 10.1088/1742-6596/1715/1/012003

M3 - Conference article

AN - SCOPUS:85100724932

VL - 1715

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012003

T2 - International Conference on Marchuk Scientific Readings 2020, MSR 2020

Y2 - 19 October 2020 through 23 October 2020

ER -