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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 9, Pages 1403–1415
DOI: https://doi.org/10.31857/S0044466921090143 (Mi zvmmf11284) 		 
General numerical methods

Numerical solving of boundary value problems on multiblock grids

S. I. Martynenkoabcd

a Institute of Problems of Chemical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia
b Joint Institute for High Temperatures, Russian Academy of Sciences, 125412, Moscow, Russia
c Bauman Moscow State Technical University, 105005, Moscow, Russia
d Central Institute of Aviation Motors, 111116, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466921090143
Abstract: Results of a theoretical analysis of the convergence of geometric multigrid algorithms in solving linear boundary value problems on two-block grids are presented. The smoothing property for a nonsymmetric iterative method with parameter and the convergence of the robust multigrid technique are proved. It is shown that the number of multigrid iterations does not depend on either the step size or the number of grid blocks. Results of computational experiments on solving a three-dimensional Dirichlet boundary value problem for a Poisson equation are given, which illustrate the theoretical analysis. This paper is of interest for developers of highly efficient algorithms to solve boundary value problems in domains with complicated geometry.
Key words: boundary value problems, multigrid methods, multiblock grids.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-46007
This study was supported by the Russian Foundation for Basic Research, project no. 21-51-46007 “Development and application of highly efficient parallel algorithms for supercomputer simulations of complex reacting flows.”
Received: 24.11.2019
Revised: 24.11.2019
Accepted: 12.05.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 9, Pages 1375–1386
DOI: https://doi.org/10.1134/S096554252109013X
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: S. I. Martynenko, “Numerical solving of boundary value problems on multiblock grids”, Zh. Vychisl. Mat. Mat. Fiz., 61:9 (2021), 1403–1415; Comput. Math. Math. Phys., 61:9 (2021), 1375–1386
Citation in format AMSBIB
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