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Matematicheskoe modelirovanie, 2022, Volume 34, Number 5, Pages 73–87
DOI: https://doi.org/10.20948/mm-2022-05-05 (Mi mm4377) 		 
Application of robust multigrid technique for parallel solution of the initial-boundary problems

S. I. Martynenkoab, I. Gökalpc, V. A. Bakhtind, M. Karacac, P. D. Toktalieva, P. A. Semeneve

a Institute of Problems of Chemical Physics of the Russian Academy of Sciences
b Joint Institute for High Temperatures of the Russian Academy of Sciences
c Middle East Technical University, Ankara, Turkey
d Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
e Central Institute of Aviation Motors, Russian Federation
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DOI: https://doi.org/10.20948/mm-2022-05-05
Abstract: The article is devoted to development of a parallel multigrid algorithm for numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on the Robust Multigrid Technique (RMT). Advantage of the proposed algorithm is opportunity of parallel solution of boundary value problems and initial-boundary value problems in unified manner using $m=1,2,3,\dots$ independent computers (threads, if parallelization technology OpenMP used). Coarse grids are generated only in space, the number of grid levels depends on the coefficient matrix condition number of the resulting system of linear algebraic equations. Point Gauss-Seidel method is used as a smoothing procedure for solving the initial-boundary value problem for the heat conductivity equation. Description of the algorithm and results of computational experiments performed using the OpenMP technology are given.
Keywords: initial boundary value problems, parallel computing, multigrid methods.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-46007 СТ_а
Scientific and Technological Research Council of Turkey (TÜBITAK) ARDEB-220N170
The work was supported by Russian Foundation for Basic Research, Grant 21-51-46007 («Development and application of highly efficient parallel algorithms for supercomputer modeling of complex reacting flows») and Scientific and Technological Research Council of Turkey (TÜBİTAK), Grant No: ARDEB-220N170.
Received: 09.03.2022
Revised: 09.03.2022
Accepted: 18.04.2022
English version:
Mathematical Models and Computer Simulations, 2022, Volume 14, Issue 6, Pages 1002–1010
DOI: https://doi.org/10.1134/S2070048222060096
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. I. Martynenko, I. Gökalp, V. A. Bakhtin, M. Karaca, P. D. Toktaliev, P. A. Semenev, “Application of robust multigrid technique for parallel solution of the initial-boundary problems”, Matem. Mod., 34:5 (2022), 73–87; Math. Models Comput. Simul., 14:6 (2022), 1002–1010
Citation in format AMSBIB
\Bibitem{MarGoeBak22}
\by S.~I.~Martynenko, I.~G\"okalp, V.~A.~Bakhtin, M.~Karaca, P.~D.~Toktaliev, P.~A.~Semenev
\paper Application of robust multigrid technique for parallel solution of the initial-boundary problems
\jour Matem. Mod.
\yr 2022
\vol 34
\issue 5
\pages 73--87
\mathnet{http://mi.mathnet.ru/mm4377}
\crossref{https://doi.org/10.20948/mm-2022-05-05}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4422587}
\transl
\jour Math. Models Comput. Simul.
\yr 2022
\vol 14
\issue 6
\pages 1002--1010
\crossref{https://doi.org/10.1134/S2070048222060096}
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