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Numerical methods and programming, 2011, Volume 12, Issue 1, Pages 110–119 (Mi vmp175)  

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
Full-text PDF (252 kB) Citations (4)
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.
Document Type: Article
UDC: 519.632
Language: Russian
Citation: V. P. Il'in, D. V. Knysh, “Parallel decomposition methods in trace spaces”, Num. Meth. Prog., 12:1 (2011), 110–119
Citation in format AMSBIB
\Bibitem{IliKny11}
\by V.~P.~Il'in, D.~V.~Knysh
\paper Parallel decomposition methods in trace spaces
\jour Num. Meth. Prog.
\yr 2011
\vol 12
\issue 1
\pages 110--119
\mathnet{http://mi.mathnet.ru/vmp175}
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  • https://www.mathnet.ru/eng/vmp/v12/i1/p110
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Numerical methods and programming
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