A Robust Multilevel Preconditioner Based on a Domain Decomposition Method for the Helmholtz Equation

doi:10.1007/s10915-019-01015-z

	A Robust Multilevel Preconditioner Based on a Domain Decomposition Method for the Helmholtz Equation
	Lu, Peipei 1; Xu, Xuejun2,3
	2019-10-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	81 期号:1 页码:291-311
摘要	In this paper, we present a robust multilevel preconditioner for the algebraic system resulting from the continuous interior penalty finite element method for the approximation of the Helmholtz equation. The key idea in this work is the replacement of traditional smoothers by the one level overlapping domain decomposition method on coarse grids. The proposed multilevel method then serves as a preconditioner in the outer GMRES iteration. Numerical results show that for fixed wave numbers, the convergence of our multilevel method is independent of the mesh size. Furthermore, the performance of the algorithm depends relatively mildly on the wave number.
关键词	Multilevel method Helmholtz equation High wave number Continuous interior penalty finite element method GMRES method Overlapping domain decomposition method
DOI	10.1007/s10915-019-01015-z
语种	英语
资助项目	National Natural Science Foundation of China[11671302] ; National Natural Science Foundation of China[11871272]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000485319000014
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/33317
专题	计算数学与科学工程计算研究所
通讯作者	Lu, Peipei
作者单位	1.Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China 2.Tongji Univ, Sch Math Sci, Shanghai 200442, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, POB 2719, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lu, Peipei,Xu, Xuejun. A Robust Multilevel Preconditioner Based on a Domain Decomposition Method for the Helmholtz Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,81(1):291-311.
APA	Lu, Peipei,&Xu, Xuejun.(2019).A Robust Multilevel Preconditioner Based on a Domain Decomposition Method for the Helmholtz Equation.JOURNAL OF SCIENTIFIC COMPUTING,81(1),291-311.
MLA	Lu, Peipei,et al."A Robust Multilevel Preconditioner Based on a Domain Decomposition Method for the Helmholtz Equation".JOURNAL OF SCIENTIFIC COMPUTING 81.1(2019):291-311.