Volume 50, Number 3, May-June 2016Special Issue – Polyhedral discretization for PDE
|Page(s)||921 - 944|
|Published online||23 May 2016|
School of Mathematical Sciences, Fudan University,
2 LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China
3 Department of Mathematics, Tongji University, Shanghai 200092, China
*** Corresponding author: firstname.lastname@example.org
Received: 15 January 2015
Revised: 24 July 2015
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.
Mathematics Subject Classification: 65N55
Key words: Robin−Robin domain decomposition method / Helmholtz equation / optimal convergence rate
The work of Wenbin Chen was supported by the Natural Science Foundation of China (11171077 and 11331004), Key Project National Science Foundation of China (91130004).
The work of Xuejun Xu was supported by the National Basic Research Program under the Grant 2011CB30971 and National Science Foundation of China (No. 11171335, 11225107).
© EDP Sciences, SMAI 2016
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