SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS

doi:10.1137/151003040

	SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS
	Hu, Qiya; Zhang, Haiyang
	2016
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	38 期号:4 页码:A2232-A2261
摘要	In this paper we are concerned with the plane wave methods for Helmholtz equations with large wave numbers. We extend the plane wave weighted least-squares (PWLS) method and the plane wave discontinuous Galerkin (PWDG) method to Helmholtz equations in inhomogeneous mediums and with mixed boundary conditions. The main goal of this paper is to construct parallel preconditioners for solving the resulting discrete systems. To this end, we design a kind of substructuring domain decomposition preconditioner for both the two-dimensional case and the three-dimensional case, which is different from the existing substructuring preconditioners. We apply the proposed preconditioner to solve the Helmholtz systems generated by the PWLS method or the PWDG method, and we find that the new preconditioners with practical coarse mesh sizes possess relatively stable convergence, i.e., the iteration counts of the corresponding iterative methods (PCG or preconditioned GMRES) increase slowly when the wave number increases (and the mesh size decreases).
关键词	Helmholtz equation large wave number plane wave discretization nonoverlapping domain decomposition parallel preconditioner iteration counts
DOI	10.1137/151003040
语种	英语
资助项目	Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000385283400014
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23762
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Qiya
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya,Zhang, Haiyang. SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016,38(4):A2232-A2261.
APA	Hu, Qiya,&Zhang, Haiyang.(2016).SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,38(4),A2232-A2261.
MLA	Hu, Qiya,et al."SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 38.4(2016):A2232-A2261.