Author:
Chen Wenbin,Liu Yongxiang,Xu Xuejun
Abstract
In this paper we present a robust Robin−Robin domain decomposition (DD) method for the Helmholtz equation with high wave number. Through choosing suitable Robin parameters on different subdomains and introducing a new relaxation parameter, we prove that the new DD method is robust, which means the convergence rate is independent of the wave number k for kh = constant and the mesh size h for fixed k. To the best of our knowledge, from the theoretical point of view, this is a first attempt to design a robust DD method for the Helmholtz equation with high wave number in the literature. Numerical results which confirm our theory are given.
Subject
Applied Mathematics,Modelling and Simulation,Numerical Analysis,Analysis,Computational Mathematics
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Helmholtz Problem. Mathematical and Numerical Aspects of Wave Propagation Phenomena,
edited by G. Cohen, L. Halpern and P. Joly. Philadelphia, SIAM (1991) 44–52.
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