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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 PublicationMATHEMATICS OF COMPUTATION
ISSN0025-5718
Volume88Issue:319Pages:2295-2324
AbstractIn 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.
KeywordJacobi-Davidson method eigenvalue problems domain decomposition method
DOI10.1090/mcom/3403
Language英语
Funding ProjectNational Natural Science Foundation of China[11671302]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000470321000009
PublisherAMER MATHEMATICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34871
Collection计算数学与科学工程计算研究所
Corresponding AuthorWang, Wei
Affiliation1.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
Recommended Citation
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.
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