AN OPTIMIZED SCHWARZ METHOD WITH RELAXATION FOR THE HELMHOLTZ EQUATION: THE NEGATIVE IMPACT OF OVERLAP

doi:10.1051/m2an/2018061

	AN OPTIMIZED SCHWARZ METHOD WITH RELAXATION FOR THE HELMHOLTZ EQUATION: THE NEGATIVE IMPACT OF OVERLAP
	Liu, Yongxiang 1,2,4; Xu, Xuejun3,4
	2019-04-10
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	53 期号:1 页码:249-268
摘要	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.
关键词	optimized Schwarz method the Helmholtz equation overlapping size
DOI	10.1051/m2an/2018061
语种	英语
资助项目	National Science Foundation of China[11671302]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000464277200004
出版者	EDP SCIENCES S A
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34513
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Yongxiang
作者单位	1.China Acad Engn Phys, Microsyst & Terahertz Res Ctr, Chengdu 610200, Sichuan, Peoples R China 2.China Acad Engn Phys, Inst Elect Engn, Mianyang 621999, Peoples R China 3.Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, POB 2719, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Yongxiang,Xu, Xuejun. AN OPTIMIZED SCHWARZ METHOD WITH RELAXATION FOR THE HELMHOLTZ EQUATION: THE NEGATIVE IMPACT OF OVERLAP[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2019,53(1):249-268.
APA	Liu, Yongxiang,&Xu, Xuejun.(2019).AN OPTIMIZED SCHWARZ METHOD WITH RELAXATION FOR THE HELMHOLTZ EQUATION: THE NEGATIVE IMPACT OF OVERLAP.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,53(1),249-268.
MLA	Liu, Yongxiang,et al."AN OPTIMIZED SCHWARZ METHOD WITH RELAXATION FOR THE HELMHOLTZ EQUATION: THE NEGATIVE IMPACT OF OVERLAP".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 53.1(2019):249-268.