TY - GEN

T1 - Comparative Analysis of Parallel Methods for Solving SLAEs in Three-Dimensional Initial-Boundary Value Problems

AU - Gladkikh, V. S.

AU - Ilin, V. P.

AU - Pekhterev, M. S.

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - Iterative methods for solving systems of linear algebraic equations with high-order sparse matrices that arise in absolutely stable implicit finite-volume approximations of three-dimensional initial-boundary value problems for the heat and mass transfer equation on unstructured grids in computational domains with a complex configuration of multiply connected piecewise smooth boundary surfaces and contrasting material properties are considered. At each time step, algebraic systems are solved using parallel preconditioned algorithms for conjugate directions in Krylov subspaces. To speed up the iterative processes, variational methods for choosing initial approximations are applied using numerical solutions from previous time steps. It is discussed how the proposed approaches can be more general formulations of problems, as well as how to increase the productivity of computational methods and technologies in the multiple solution of algebraic systems with sequentially determined different right-hand sides and with the scalable parallelization of algorithms based on the additive methods of domain decomposition. The efficiency of the proposed approaches is investigated for the implicit Euler and Crank–Nicholson schemes based on the results of numerical experiments on a representative series of methodological problems.

AB - Iterative methods for solving systems of linear algebraic equations with high-order sparse matrices that arise in absolutely stable implicit finite-volume approximations of three-dimensional initial-boundary value problems for the heat and mass transfer equation on unstructured grids in computational domains with a complex configuration of multiply connected piecewise smooth boundary surfaces and contrasting material properties are considered. At each time step, algebraic systems are solved using parallel preconditioned algorithms for conjugate directions in Krylov subspaces. To speed up the iterative processes, variational methods for choosing initial approximations are applied using numerical solutions from previous time steps. It is discussed how the proposed approaches can be more general formulations of problems, as well as how to increase the productivity of computational methods and technologies in the multiple solution of algebraic systems with sequentially determined different right-hand sides and with the scalable parallelization of algorithms based on the additive methods of domain decomposition. The efficiency of the proposed approaches is investigated for the implicit Euler and Crank–Nicholson schemes based on the results of numerical experiments on a representative series of methodological problems.

KW - implicit schemes

KW - initial-boundary value problem

KW - iterative processes

KW - Krylov subspaces

KW - least squares method

KW - numerical experiments

UR - http://www.scopus.com/inward/record.url?scp=85135020630&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2763bdda-8ea5-3629-bcd8-6081e9afabc1/

U2 - 10.1007/978-3-031-11623-0_5

DO - 10.1007/978-3-031-11623-0_5

M3 - Conference contribution

AN - SCOPUS:85135020630

SN - 9783031116223

T3 - Communications in Computer and Information Science

SP - 59

EP - 72

BT - Parallel Computational Technologies - 16th International Conference, PCT 2022, Revised Selected Papers

A2 - Sokolinsky, Leonid

A2 - Zymbler, Mikhail

PB - Springer Science and Business Media Deutschland GmbH

T2 - 16th International Conference on Parallel Computational Technologies, PCT 2022

Y2 - 29 March 2022 through 31 March 2022

ER -