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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 for and the mesh size for fixed . 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.
Chen, Wenbin 1 ; Liu, Yongxiang 2 ; Xu, Xuejun 2, 3
@article{M2AN_2016__50_3_921_0,
author = {Chen, Wenbin and Liu, Yongxiang and Xu, Xuejun},
title = {A robust domain decomposition method for the {Helmholtz} equation with high wave number},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {921--944},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/m2an/2015058},
zbl = {1361.65093},
mrnumber = {3507279},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015058/}
}
TY - JOUR AU - Chen, Wenbin AU - Liu, Yongxiang AU - Xu, Xuejun TI - A robust domain decomposition method for the Helmholtz equation with high wave number JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 921 EP - 944 VL - 50 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015058/ DO - 10.1051/m2an/2015058 LA - en ID - M2AN_2016__50_3_921_0 ER -
%0 Journal Article %A Chen, Wenbin %A Liu, Yongxiang %A Xu, Xuejun %T A robust domain decomposition method for the Helmholtz equation with high wave number %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 921-944 %V 50 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015058/ %R 10.1051/m2an/2015058 %G en %F M2AN_2016__50_3_921_0
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. http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015058/
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