Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
نویسندگان
چکیده
منابع مشابه
Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directio...
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The principle of sweeping to accelerate the solution of wave propagation problems has recently retained much interest, yet with different approaches (Engquist and Ying [2011], Stolk [2013]). We recently proposed a preconditioner for the optimized Schwarz algorithm, based on a propagation of information using a double sequence of subproblems solves, or sweeps (Vion et al. [2013], Vion and Geuzai...
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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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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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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2014
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2014.02.015