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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 конференцийстатья в сборнике материалов конференциинаучнаяРецензирование

Harvard

Batalov, M, Gurieva, Y, Ilyin, V & Petukhov, A 2023, On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations. в 17th International Scientific Conference on Parallel Computational Technologies, PCT 2023. Springer Science and Business Media Deutschland GmbH, стр. 93-109, 17th International Conference "Parallel Computational Technologies", Санкт-Петербург, Российская Федерация, 28.03.2024. https://doi.org/10.1007/978-3-031-38864-4_7

APA

Batalov, M., Gurieva, Y., Ilyin, V., & Petukhov, A. (2023). On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations. в 17th International Scientific Conference on Parallel Computational Technologies, PCT 2023 (стр. 93-109). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-38864-4_7

Vancouver

Batalov M, Gurieva Y, Ilyin V, Petukhov A. On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations. в 17th International Scientific Conference on Parallel Computational Technologies, PCT 2023. Springer Science and Business Media Deutschland GmbH. 2023. стр. 93-109 doi: 10.1007/978-3-031-38864-4_7

Author

Batalov, Maxim ; Gurieva, Yana ; Ilyin, Valery и др. / On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations. 17th International Scientific Conference on Parallel Computational Technologies, PCT 2023. Springer Science and Business Media Deutschland GmbH, 2023. стр. 93-109

BibTeX

@inproceedings{d06b31873f4b45ceaa7759615924d527,
title = "On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations",
abstract = "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.",
author = "Maxim Batalov and Yana Gurieva and Valery Ilyin and Artyom Petukhov",
year = "2023",
doi = "10.1007/978-3-031-38864-4_7",
language = "English",
isbn = "9783031388637",
pages = "93--109",
booktitle = "17th International Scientific Conference on Parallel Computational Technologies, PCT 2023",
publisher = "Springer Science and Business Media Deutschland GmbH",
address = "Germany",
note = "17th International Conference {"}Parallel Computational Technologies{"}, PCT 2023 ; Conference date: 28-03-2024 Through 30-03-2024",

}

RIS

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