| Issue |
ESAIM: M2AN
Volume 50, Number 3, May-June 2016
Special Issue – Polyhedral discretization for PDE
|
|
|---|---|---|
| Page(s) | 921 - 944 | |
| Section | Regular articles | |
| DOI | https://doi.org/10.1051/m2an/2015058 | |
| Published online | 23 May 2016 | |
A robust domain decomposition method for the Helmholtz equation with high wave number∗,∗∗
1
School of Mathematical Sciences, Fudan University,
Shanghai
200437,
China
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: yxliu@lsec.cc.ac.cn
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).
© EDP Sciences, SMAI 2016
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