Geodesic
A robust domain decomposition method for the Helmholtz equation with high wave number
Chen, Wenbin1 ; Liu, Yongxiang2 ; Xu, Xuejun2, 3
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
ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 921-944

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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.

Reçu le :
DOI : 10.1051/m2an/2015058
Classification : 65N55
Keywords: Robin−Robin domain decomposition method, Helmholtz equation, optimal convergence rate

Chen, Wenbin 1 ; Liu, Yongxiang 2 ; Xu, Xuejun 2, 3

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 
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     title = {A robust domain decomposition method for the {Helmholtz} equation with high wave number},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {921--944},
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Chen, Wenbin; Liu, Yongxiang; Xu, Xuejun. A robust domain decomposition method for the Helmholtz equation with high wave number. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 921-944. doi: 10.1051/m2an/2015058

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