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Об итерационном решении задачи Стокса. / Гурин, Алексей Михайлович; Ильин, Валерий Павлович; Козлов, Дмитрий Иванович et al.

In: Сибирские электронные математические известия, Vol. 22, No. 1, 2025, p. А102-А120.

Research output: Contribution to journal › Article › peer-review

Harvard

Гурин, АМ, Ильин, ВП, Козлов, ДИ & Кузьмин, ЕА 2025, 'Об итерационном решении задачи Стокса', Сибирские электронные математические известия, vol. 22, no. 1, pp. А102-А120. https://doi.org/10.33048/semi.2025.22.A08

APA

Гурин, А. М., Ильин, В. П., Козлов, Д. И., & Кузьмин, Е. А. (2025). Об итерационном решении задачи Стокса. Сибирские электронные математические известия, 22(1), А102-А120. https://doi.org/10.33048/semi.2025.22.A08

Vancouver

Гурин АМ, Ильин ВП, Козлов ДИ, Кузьмин ЕА. Об итерационном решении задачи Стокса. Сибирские электронные математические известия. 2025;22(1):А102-А120. doi: 10.33048/semi.2025.22.A08

Author

Гурин, Алексей Михайлович ; Ильин, Валерий Павлович ; Козлов, Дмитрий Иванович et al. / Об итерационном решении задачи Стокса. In: Сибирские электронные математические известия. 2025 ; Vol. 22, No. 1. pp. А102-А120.

BibTeX

@article{f38e7449faa54c55aa38bd5f8eaa4eb4,
title = "Об итерационном решении задачи Стокса",
abstract = " Block preconditioned iterative conjugate gradient methods for solving the three-dimensional Stokes problem are investigated. A formulation with a computational domain in the form of a parallelepiped is considered. Standard approximations on a cubic staggered grid, seven-point and two-point for the Laplace and derivative operators are used. The resulting saddle-type SLAE is regularized to ensure the uniqueness of the solution. The block preconditioner is constructed by the method of incomplete factorization with diagonal compensation and using band approximations for matrices inverse to the Schur complement and the grid Laplace operator, as well as using an algebraic multigrid algorithm. Examples of numerical experiments on a representative series of methodological problems using parallel algorithms on di erent numbers of processors are given. The issues of generalizing the proposed approaches to broader classes of problems are considered.",
keywords = ":Stokes problem, large sparse SLAEs, iterative preconditioned methods, Krylov subspace, Schur complement",
author = "Гурин, {Алексей Михайлович} and Ильин, {Валерий Павлович} and Козлов, {Дмитрий Иванович} and Кузьмин, {Евгений Алексеевич}",
note = "Об итерационном решении задачи Стокса / А. М. Гурин, В. П. Ильин, Д. И. Козлов, Е. А. Кузьмин // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. А102-А120. – DOI 10.33048/semi.2025.22.A08",
year = "2025",
doi = "10.33048/semi.2025.22.A08",
language = "русский",
volume = "22",
pages = "А102--А120",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Об итерационном решении задачи Стокса

AU - Гурин, Алексей Михайлович

AU - Ильин, Валерий Павлович

AU - Козлов, Дмитрий Иванович

AU - Кузьмин, Евгений Алексеевич

N1 - Об итерационном решении задачи Стокса / А. М. Гурин, В. П. Ильин, Д. И. Козлов, Е. А. Кузьмин // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. А102-А120. – DOI 10.33048/semi.2025.22.A08

PY - 2025

Y1 - 2025

N2 - Block preconditioned iterative conjugate gradient methods for solving the three-dimensional Stokes problem are investigated. A formulation with a computational domain in the form of a parallelepiped is considered. Standard approximations on a cubic staggered grid, seven-point and two-point for the Laplace and derivative operators are used. The resulting saddle-type SLAE is regularized to ensure the uniqueness of the solution. The block preconditioner is constructed by the method of incomplete factorization with diagonal compensation and using band approximations for matrices inverse to the Schur complement and the grid Laplace operator, as well as using an algebraic multigrid algorithm. Examples of numerical experiments on a representative series of methodological problems using parallel algorithms on di erent numbers of processors are given. The issues of generalizing the proposed approaches to broader classes of problems are considered.

AB - Block preconditioned iterative conjugate gradient methods for solving the three-dimensional Stokes problem are investigated. A formulation with a computational domain in the form of a parallelepiped is considered. Standard approximations on a cubic staggered grid, seven-point and two-point for the Laplace and derivative operators are used. The resulting saddle-type SLAE is regularized to ensure the uniqueness of the solution. The block preconditioner is constructed by the method of incomplete factorization with diagonal compensation and using band approximations for matrices inverse to the Schur complement and the grid Laplace operator, as well as using an algebraic multigrid algorithm. Examples of numerical experiments on a representative series of methodological problems using parallel algorithms on di erent numbers of processors are given. The issues of generalizing the proposed approaches to broader classes of problems are considered.

KW - :Stokes problem

KW - large sparse SLAEs

KW - iterative preconditioned methods

KW - Krylov subspace

KW - Schur complement

UR - https://math-semr.ru/sites/math-semr.ru/files/2025-08/A102-A120.pdf

U2 - 10.33048/semi.2025.22.A08

DO - 10.33048/semi.2025.22.A08

M3 - статья

VL - 22

SP - А102-А120

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 71568112