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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
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.
Received: 24.11.2019 Revised: 24.11.2019 Accepted: 12.05.2020
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11284 https://www.mathnet.ru/eng/zvmmf/v61/i9/p1403
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