NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS

doi:10.1137/15M1022963

	NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS
	Hu, Qiya1,2 ; Li, Xuan 3
	2017
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	39 期号:4 页码:A1675-A1709
摘要	In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method and the plane wave discontinuous Galerkin (PWDG) method. The main goal of this paper is to construct multilevel parallel preconditioners for solving the resulting Helmholtz systems. To this end, we first build a multilevel space decomposition for the plane wave discretization space based on a multilevel overlapping domain decomposition method. Then, corresponding to the space decomposition, we construct an additive multilevel preconditioner for the underlying Helmholtz systems. Further, we design both additive and multiplicative multilevel preconditioners with smoothers, which are different from the standard multigrid preconditioners. We apply the proposed multilevel preconditioners with a constant coarsest mesh size to solve two-dimensional Helmholtz systems generated by the PWLS method or PWDG method, and we find that the new preconditioners possess nearly stable convergence; i.e., the iteration counts of the preconditioned iterative methods (PCG or PGMRES) with the preconditioners increase very slowly when the wave number increases (and the fine mesh size decreases).
关键词	Helmholtz equation large wave numbers plane wave methods multilevel overlapping domain decomposition multilevel overlapping preconditioner smoothers
DOI	10.1137/15M1022963
语种	英语
资助项目	National Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000408922600030
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/26535
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	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing, Peoples R China 3.Huawei Technol CO LTD, 101 Software Ave, Nanjing 210012, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya,Li, Xuan. NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2017,39(4):A1675-A1709.
APA	Hu, Qiya,&Li, Xuan.(2017).NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,39(4),A1675-A1709.
MLA	Hu, Qiya,et al."NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 39.4(2017):A1675-A1709.