Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations. / Batalov, Maxim; Gurieva, Yana; Ilyin, Valery и др.
17th International Scientific Conference on Parallel Computational Technologies, PCT 2023. Springer Science and Business Media Deutschland GmbH, 2023. стр. 93-109.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations
AU - Batalov, Maxim
AU - Gurieva, Yana
AU - Ilyin, Valery
AU - Petukhov, Artyom
N1 - Conference code: 17
PY - 2023
Y1 - 2023
N2 - In this paper, we consider algebraic multigrid methods (AMG) for solving symmetric positive-definite systems of linear algebraic equations (SLAE) with sparse high-order matrices arising from finite difference approximations of two- and three-dimensional boundary value problems on regular grids. Also, we investigate iterative algorithms in Krylov subspaces with preconditioning based on incomplete factorization with recursive ordering of variables defined on a sequence of embedded grids. We use the conjugate direction method, in which the solution of the auxiliary SLAE with its preconditioning matrix includes the conventional stages of restriction, coarse-grid correction, and prolongation. We show how additional preconditioning based on the principles of symmetric successive over-relaxation (SSOR) allows carrying out presmoothing and postsmoothing operations. Also, we discuss the parallelization effectiveness of the proposed algorithms with different numbers of embedded grids. Furthermore, we present the results of preliminary experimental investigations demonstrating the efficiency of the implemented methods and analyze the possibilities of generalizing the developed approaches to solving a wider class of problems.
AB - In this paper, we consider algebraic multigrid methods (AMG) for solving symmetric positive-definite systems of linear algebraic equations (SLAE) with sparse high-order matrices arising from finite difference approximations of two- and three-dimensional boundary value problems on regular grids. Also, we investigate iterative algorithms in Krylov subspaces with preconditioning based on incomplete factorization with recursive ordering of variables defined on a sequence of embedded grids. We use the conjugate direction method, in which the solution of the auxiliary SLAE with its preconditioning matrix includes the conventional stages of restriction, coarse-grid correction, and prolongation. We show how additional preconditioning based on the principles of symmetric successive over-relaxation (SSOR) allows carrying out presmoothing and postsmoothing operations. Also, we discuss the parallelization effectiveness of the proposed algorithms with different numbers of embedded grids. Furthermore, we present the results of preliminary experimental investigations demonstrating the efficiency of the implemented methods and analyze the possibilities of generalizing the developed approaches to solving a wider class of problems.
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85172696240&origin=inward&txGid=32ddc70d45869f960dc68cd4bcb394f0
UR - https://www.mendeley.com/catalogue/8db3f270-a597-3b89-8f35-a0ddf5e67433/
U2 - 10.1007/978-3-031-38864-4_7
DO - 10.1007/978-3-031-38864-4_7
M3 - Conference contribution
SN - 9783031388637
SP - 93
EP - 109
BT - 17th International Scientific Conference on Parallel Computational Technologies, PCT 2023
PB - Springer Science and Business Media Deutschland GmbH
T2 - 17th International Conference "Parallel Computational Technologies"
Y2 - 28 March 2024 through 30 March 2024
ER -
ID: 59179138