CSpace
A PARALLEL AUGMENTED SUBSPACE METHOD FOR EIGENVALUE PROBLEMS
Xu, Fei1; Xie, Hehu2,3; Zhang, Ning4
2020
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume42Issue:5Pages:A2655-A2677
AbstractA type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in the multigrid method, solving the eigenvalue problem in the finest space is decomposed into solving the standard linear boundary value problems and very-low-dimensional eigenvalue problems. The computational efficiency can be improved since there is no direct eigenvalue solving in the finest space and the multigrid method can act as the solver for the deduced linear boundary value problems. Furthermore, for different eigenvalues, the corresponding boundary value problem and low-dimensional eigenvalue problem can be solved in the parallel way since they are independent of each other and there exists no data exchanging. This property means that we do not need to do the orthogonalization in the highest-dimensional spaces. This is the main aim of this paper since avoiding orthogonalization can improve the scalability of the proposed numerical method. Some numerical examples are provided to validate the proposed parallel augmented subspace method.
Keywordeigenvalue problems parallel augmented subspace method multigrid method parallel computing
DOI10.1137/19M128452X
Indexed BySCI
Language英语
Funding ProjectNational Key Research and Development Program of China[2019YFA0709601] ; National Natural Science Foundations of China (NSFC)[11771434] ; National Natural Science Foundations of China (NSFC)[11801021] ; National Natural Science Foundations of China (NSFC)[91730302] ; National Natural Science Foundations of China (NSFC)[91630201] ; National Center for Mathematics and Interdisciplinary Science, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000600650100028
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/57883
Collection中国科学院数学与系统科学研究院
Corresponding AuthorXu, Fei
Affiliation1.Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC,NCMIS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Chinese Acad Sci, Inst Elect Engn, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Xu, Fei,Xie, Hehu,Zhang, Ning. A PARALLEL AUGMENTED SUBSPACE METHOD FOR EIGENVALUE PROBLEMS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(5):A2655-A2677.
APA Xu, Fei,Xie, Hehu,&Zhang, Ning.(2020).A PARALLEL AUGMENTED SUBSPACE METHOD FOR EIGENVALUE PROBLEMS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,42(5),A2655-A2677.
MLA Xu, Fei,et al."A PARALLEL AUGMENTED SUBSPACE METHOD FOR EIGENVALUE PROBLEMS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 42.5(2020):A2655-A2677.
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