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 ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS Wang, Wei1,2; Xu, Xuejun2,3 2019-09-01 Source Publication MATHEMATICS OF COMPUTATION ISSN 0025-5718 Volume 88Issue:319Pages:2295-2324 Abstract 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. Keyword Jacobi-Davidson method eigenvalue problems domain decomposition method DOI 10.1090/mcom/3403 Language 英语 Funding Project National Natural Science Foundation of China[11671302] WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000470321000009 Publisher AMER MATHEMATICAL SOC Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/34871 Collection 计算数学与科学工程计算研究所 Corresponding Author Wang, Wei Affiliation 1.Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, POB 2719, Beijing 100190, Peoples R China3.Tongji Univ, Sch Math Sci, Shanghai 200442, Peoples R China Recommended CitationGB/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.
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