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On the minimal residual methods for solving diffusionconvection SLAEs. / Il'in, V. P.; Kozlov, D. I.; Petukhov, A. V.

In: Journal of Physics: Conference Series, Vol. 2099, No. 1, 012005, 13.12.2021.

Research output: Contribution to journalConference articlepeer-review

Harvard

Il'in, VP, Kozlov, DI & Petukhov, AV 2021, 'On the minimal residual methods for solving diffusionconvection SLAEs', Journal of Physics: Conference Series, vol. 2099, no. 1, 012005. https://doi.org/10.1088/1742-6596/2099/1/012005

APA

Il'in, V. P., Kozlov, D. I., & Petukhov, A. V. (2021). On the minimal residual methods for solving diffusionconvection SLAEs. Journal of Physics: Conference Series, 2099(1), [012005]. https://doi.org/10.1088/1742-6596/2099/1/012005

Vancouver

Il'in VP, Kozlov DI, Petukhov AV. On the minimal residual methods for solving diffusionconvection SLAEs. Journal of Physics: Conference Series. 2021 Dec 13;2099(1):012005. doi: 10.1088/1742-6596/2099/1/012005

Author

Il'in, V. P. ; Kozlov, D. I. ; Petukhov, A. V. / On the minimal residual methods for solving diffusionconvection SLAEs. In: Journal of Physics: Conference Series. 2021 ; Vol. 2099, No. 1.

BibTeX

@article{c8b9c683b4c24a7daabb8b568282551b,
title = "On the minimal residual methods for solving diffusionconvection SLAEs",
abstract = "The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA - orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT - preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.",
author = "Il'in, {V. P.} and Kozlov, {D. I.} and Petukhov, {A. V.}",
note = "Funding Information: This work was supported by grants from the Russian Scientific Foundation No 19-11-00048. Publisher Copyright: {\textcopyright} 2021 Institute of Physics Publishing. All rights reserved.; International Conference on Marchuk Scientific Readings 2021, MSR 2021 ; Conference date: 04-10-2021 Through 08-10-2021",
year = "2021",
month = dec,
day = "13",
doi = "10.1088/1742-6596/2099/1/012005",
language = "English",
volume = "2099",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - On the minimal residual methods for solving diffusionconvection SLAEs

AU - Il'in, V. P.

AU - Kozlov, D. I.

AU - Petukhov, A. V.

N1 - Funding Information: This work was supported by grants from the Russian Scientific Foundation No 19-11-00048. Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved.

PY - 2021/12/13

Y1 - 2021/12/13

N2 - The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA - orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT - preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.

AB - The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA - orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT - preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.

UR - http://www.scopus.com/inward/record.url?scp=85123677223&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/2099/1/012005

DO - 10.1088/1742-6596/2099/1/012005

M3 - Conference article

AN - SCOPUS:85123677223

VL - 2099

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012005

T2 - International Conference on Marchuk Scientific Readings 2021, MSR 2021

Y2 - 4 October 2021 through 8 October 2021

ER -

ID: 35378463