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
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