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Volume 13, Issue 1
Fast Solvers for Systems of Linear Equations with Block-Band Matrices

B.Ya. Steinberg, O.B. Steinberg, P.A. Oganesyan, A.A. Vasilenko, V.V. Veselovskiy & N.A. Zhivykh

DOI: 10.4208/eajam.300921.210522

East Asian J. Appl. Math., 13 (2023), pp. 47-58.

Published online: 2023-01

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  • Abstract

This article deals with parallel iterative algorithms for linear systems with block-band matrices. The algorithms can be used in mathematical modeling of the problems involving finite difference and finite element methods. The solvers are adjusted to the problem and to the computing systems, which use special precompilers. Applications of the algorithms to the ACELAN-COMPOS software package focused on the new material modeling, is described. To achieve a high performance, both parallel programming techniques and the optimization of the processor memory hierarchy are used. The results of numerical experiments confirm the efficiency of the methods and algorithms.

  • Keywords

High performance computing, parallel computing, iterative algorithm, sparse matrix, system of linear algebraic equations.

  • AMS Subject Headings

65F08, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-47, author = {Steinberg , B.Ya.Steinberg , O.B.Oganesyan , P.A.Vasilenko , A.A.Veselovskiy , V.V. and Zhivykh , N.A.}, title = {Fast Solvers for Systems of Linear Equations with Block-Band Matrices}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {47--58}, abstract = {

This article deals with parallel iterative algorithms for linear systems with block-band matrices. The algorithms can be used in mathematical modeling of the problems involving finite difference and finite element methods. The solvers are adjusted to the problem and to the computing systems, which use special precompilers. Applications of the algorithms to the ACELAN-COMPOS software package focused on the new material modeling, is described. To achieve a high performance, both parallel programming techniques and the optimization of the processor memory hierarchy are used. The results of numerical experiments confirm the efficiency of the methods and algorithms.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.300921.210522 }, url = {http://global-sci.org/intro/article_detail/eajam/21301.html} }
TY - JOUR T1 - Fast Solvers for Systems of Linear Equations with Block-Band Matrices AU - Steinberg , B.Ya. AU - Steinberg , O.B. AU - Oganesyan , P.A. AU - Vasilenko , A.A. AU - Veselovskiy , V.V. AU - Zhivykh , N.A. JO - East Asian Journal on Applied Mathematics VL - 1 SP - 47 EP - 58 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.300921.210522 UR - https://global-sci.org/intro/article_detail/eajam/21301.html KW - High performance computing, parallel computing, iterative algorithm, sparse matrix, system of linear algebraic equations. AB -

This article deals with parallel iterative algorithms for linear systems with block-band matrices. The algorithms can be used in mathematical modeling of the problems involving finite difference and finite element methods. The solvers are adjusted to the problem and to the computing systems, which use special precompilers. Applications of the algorithms to the ACELAN-COMPOS software package focused on the new material modeling, is described. To achieve a high performance, both parallel programming techniques and the optimization of the processor memory hierarchy are used. The results of numerical experiments confirm the efficiency of the methods and algorithms.

Steinberg , B.Ya.Steinberg , O.B.Oganesyan , P.A.Vasilenko , A.A.Veselovskiy , V.V. and Zhivykh , N.A.. (2023). Fast Solvers for Systems of Linear Equations with Block-Band Matrices. East Asian Journal on Applied Mathematics. 13 (1). 47-58. doi:10.4208/eajam.300921.210522
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