ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS

doi:10.1090/mcom/3403

	ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS
	Wang, Wei 1,2; Xu, Xuejun2,3
	2019-09-01
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	88 期号:319 页码:2295-2324
摘要	In this paper, we shall give a rigorous theoretical analysis of the two-level preconditioned Jacobi-Davidson method for solving the large scale discrete elliptic eigenvalue problems, which was essentially proposed by Zhao, Hwang, and Cai in 2016. Focusing on eliminating the error components in the orthogonal complement space of the target eigenspace, we find that the method could be extended to the case of the 2mth order elliptic operator (m = 1,2). By choosing a suitable coarse space, we prove that the method holds a good scalability and we obtain the error reduction gamma = c(1-C delta(2m-1)/H2m-1) in each iteration, where C is a constant independent of the mesh size h and the diameter of subdomains H, delta is the overlapping size among the subdomains, and c -> 1 decreasingly as H -> 0. Moreover, the method does not need any assumption between H and h. Numerical results supporting our theory are given.
关键词	Jacobi-Davidson method eigenvalue problems domain decomposition method
DOI	10.1090/mcom/3403
语种	英语
资助项目	National Natural Science Foundation of China[11671302]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000470321000009
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34871
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Wei
作者单位	1.Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, POB 2719, Beijing 100190, Peoples R China 3.Tongji Univ, Sch Math Sci, Shanghai 200442, Peoples R China
推荐引用方式 GB/T 7714	Wang, Wei,Xu, Xuejun. ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS[J]. MATHEMATICS OF COMPUTATION,2019,88(319):2295-2324.
APA	Wang, Wei,&Xu, Xuejun.(2019).ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS.MATHEMATICS OF COMPUTATION,88(319),2295-2324.
MLA	Wang, Wei,et al."ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS".MATHEMATICS OF COMPUTATION 88.319(2019):2295-2324.