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Numerical methods and programming, 2011, Volume 12, Issue 1, Pages 110–119
(Mi vmp175)
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This article is cited in 3 scientific papers (total in 4 papers)
Вычислительные методы и приложения
Parallel decomposition methods in trace spaces
V. P. Il'ina, D. V. Knyshb a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
Two-level iterative Krylov's conjugate direction methods are proposed for the traces
of solutions on the internal boundaries of subdomains in the case of spatial
decomposition of multidimensional boundary value problems. The global iterative process
consists in solving the Poincare–Steklov equation with overlapping and without overlapping
of subdomains. The local iterative process consists in solving independent
auxiliary problems in the subdomains. The effect of the subdomain overlapping
size, the types of iterated internal boundary conditions, and the accuracy of
the solutions to the auxiliary boundary value problems on the convergence rate
of the decomposition methods is experimentally studied. Some results of
solving a number of representative model boundary value problems are
discussed. These results confirm the efficiency of parallelization of the
decomposition methods on multiprocessor computing system with distributed and
shared memory, depending on the chosen values of computational parameters of
the iterative processes.
Keywords:
Poincare-Steklov equation; overlapping; decomposition; Poisson equation; alternative Schwarz method.
Citation:
V. P. Il'in, D. V. Knysh, “Parallel decomposition methods in trace spaces”, Num. Meth. Prog., 12:1 (2011), 110–119
Linking options:
https://www.mathnet.ru/eng/vmp175 https://www.mathnet.ru/eng/vmp/v12/i1/p110
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