Optimized Schwarz Methods for Circular Domain Decompositions with Overlap
نویسندگان
چکیده
منابع مشابه
Optimized Schwarz Methods for Circular Domain Decompositions with Overlap
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...
متن کاملOptimized Schwarz methods with nonoverlapping circular domain decomposition
While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interf...
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...
متن کاملOptimized 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...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2014
ISSN: 0036-1429,1095-7170
DOI: 10.1137/130946125