Optimized Schwarz Methods without Overlap for the Helmholtz Equation
نویسندگان
چکیده
منابع مشابه
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
The classical Schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel. Convergence is achieved through overlap of the subdomains. We study in this paper a variant of the Schwarz method which converges without overlap for the Helmholtz equation. We show that the key ingredients for such an algorithm are the transmission conditions. We derive o...
متن کاملOptimized Schwarz Methods with Overlap for the Helmholtz Equation
For the Helmholtz equation, simple absorbing conditions of the form ∂n − iω were proposed as transmission condition (TC) in Schwarz methods first without overlap in [4], and later also with overlap, see [3, 12]. More advanced TCs can also be used, see e.g. [11, 14, 2]. Furthermore, parameters can be introduced into TCs and then optimized for rapid convergence, which led to the so called optimiz...
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An asynchronous version of the optimized Schwarz method for the solution of differential equations on a parallel computational environment is studied. In a one-way subdivision of the computational domain, with and without overlap, the method is shown to converge when the optimal artificial interface conditions are used. Convergence is also proved for the Laplacian operator under very mild condi...
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Optimized Schwarz methods are based on transmission conditions between subdomains which are optimized for the problem class that is being solved. Such optimizations have been performed for many different types of partial differential equations, but were almost exclusively based on the assumption of straight interfaces. We study in this paper the influence of curvature on the optimization, and w...
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In previous work (Y. Boubendir, X. Antoine and C. Geuzaine, A quasi-optimal nonoverlapping domain decomposition algorithm for the Helmholtz equation, JCP, 231, pp. 262-280, 2012), it was shown how a Domain Decomposition Method (DDM) formulation of the Helmholtz problem, using impedance-matching boundary conditions, can be set up and accelerated with a Krylov solver. This optimized Schwarz algor...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2002
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827501387012