Research output: Contribution to journal › Conference article › peer-review
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 journal › Conference article › peer-review
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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