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Num. Meth. Prog., 2014, Volume 15, Issue 3, Pages 476–486 (Mi vmp265)  

Influence of perturbations in transmission conditions on the convergence of the domain decomposition method for the Helmholtz equation

A. F. Zaitseva, V. V. Lisitsa

A. A. Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The domain decomposition is a widely used technique applied in parallel iterative solvers of the Helmholtz equation with the convergence rate controlled by the quality of transmission conditions. The optimal conditions are those based on the Dirichlet-to-Neumann map. However, if grid-based numerical methods are used to solve the Helmholtz equation, this map needs to be localized, which induces artificial grid-independent perturbations in the transmission conditions. In this paper it is proved that if the perturbations are nonsymmetric, i.e. different errors are induced in the adjoint subdomains, then the domain decomposition method converges to a solution of a problem differing from the original one. In other words, there exists an irreducible error.

Keywords: domain decomposition method, Helmholtz equation, Dirichlet-to-Neumann map, finite difference method, method of small perturbations, convergence of iterative processes.

Full text: PDF file (241 kB)
UDC: 550.341
Received: 15.07.2014

Citation: A. F. Zaitseva, V. V. Lisitsa, “Influence of perturbations in transmission conditions on the convergence of the domain decomposition method for the Helmholtz equation”, Num. Meth. Prog., 15:3 (2014), 476–486

Citation in format AMSBIB
\Bibitem{ZaiLis14}
\by A.~F.~Zaitseva, V.~V.~Lisitsa
\paper Influence of perturbations in transmission conditions on the convergence of the domain decomposition method for the Helmholtz equation
\jour Num. Meth. Prog.
\yr 2014
\vol 15
\issue 3
\pages 476--486
\mathnet{http://mi.mathnet.ru/vmp265}


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