| Issue |
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
|
|
|---|---|---|
| Page(s) | 249 - 268 | |
| DOI | https://doi.org/10.1051/m2an/2018061 | |
| Published online | 10 April 2019 | |
An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap
1
Microsystems and Terahertz Research Center, China Academy of Engineering Physics, Chengdu 610200, China
2
Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621999, China
3
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
4
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China
* Corresponding author: yxliu@lsec.cc.ac.cn
Received:
24
August
2017
Accepted:
16
October
2018
In this paper we study how the overlapping size influences the convergence rate of an optimized Schwarz domain decomposition (DD) method with relaxation in the two subdomain case for the Helmholtz equation. Through choosing suitable parameters, we find that the convergence rate is independent of the wave number k and mesh size h, but sensitively depends on the overlapping size. Furthermore, by careful analysis, we obtain that the convergence behavior deteriorates with the increase of the overlapping size. Numerical results which confirm our theory are given.
Mathematics Subject Classification: 65N55
Key words: optimized Schwarz method / the Helmholtz equation / overlapping size
© EDP Sciences, SMAI 2019
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