A ROBUST DOMAIN DECOMPOSITION METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBER

被引：15

作者：

Chen, Wenbin ^{[1
]}

Liu, Yongxiang ^{[2
]}

Xu, Xuejun ^{[2
,3
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200437, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, POB 2719, Beijing 100190, Peoples R China

[3] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2016年 / 50卷 / 03期

基金：

美国国家科学基金会;

关键词：

Robin-Robin domain decomposition method; Helmholtz equation; optimal convergence rate; OPTIMIZED SCHWARZ METHODS; SPECTRAL-ANALYSIS; CONVERGENCE RATE;

D O I：

10.1051/m2an/2015058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：921 / 944

页数：24

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