Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem

JOURNAL OF COMPUTATIONAL PHYSICS

卷:266

Article

Vion, A.¹  Geuzaine, C.¹ 

[1] Univ Liege, Dept Elect Engn & Comp Sci, Montefiore Inst B28, B-4000 Liege, Belgium

关键词: Domain decomposition method;    Helmholtz equation;    Preconditioners;    Iterative solvers;    Acoustic scattering;    Short-wave problem;    Finite element method;   

DOI  :  10.1016/j.jcp.2014.02.015

来源: Elsevier

【 摘 要 】

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 directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free