EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS

doi:10.1137/16M1084791

	EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS
	Hu, Qiya1,2 ; Li, Xuan 3
	2017
发表期刊	MULTISCALE MODELING & SIMULATION
ISSN	1540-3459
卷号	15 期号:3 页码:1242-1266
摘要	In this paper we are concerned with solvers for the systems arising from the plane wave discretizations of three dimensional Helmholtz equations with large wave numbers. For simplicity, we consider only the plane wave weighted least squares (PWLS) method for Helmholtz equations. The main goal of this paper is to construct efficient multilevel 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 overlapping domain decompositions. Then, corresponding to the space decomposition, we construct two additive multilevel preconditioners with smoothers for the underlying Helmholtz systems. In these preconditioners, each subproblem to be solved has a very small number of degrees of freedom, which just equals the number of the plane wave basis functions on one element. Moreover, the preconditioners possess the optimal computational complexity per iteration. We apply the proposed multilevel preconditioners with a constant coarse mesh size to solve the systems generated by the PWLS discretization for three dimensional Helmholtz equations, and we find that the new preconditioners possess nearly stable convergence, i.e., the iteration counts of the preconditioned CG methods 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 overlapping domain decomposition multilevel preconditioners 3-level smoothers
DOI	10.1137/16M1084791
语种	英语
资助项目	Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000412162400007
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/26680
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 Aveune, Nanjing 210012, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya,Li, Xuan. EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS[J]. MULTISCALE MODELING & SIMULATION,2017,15(3):1242-1266.
APA	Hu, Qiya,&Li, Xuan.(2017).EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS.MULTISCALE MODELING & SIMULATION,15(3),1242-1266.
MLA	Hu, Qiya,et al."EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS".MULTISCALE MODELING & SIMULATION 15.3(2017):1242-1266.