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A MULTILEVEL NEWTON'S METHOD FOR EIGENVALUE PROBLEMS
He, Yunhui1; Li, Yu2; Xie, Hehu3,4; You, Chun'Guang5; Zhang, Ning3,4
2018-06-01
Source PublicationAPPLICATIONS OF MATHEMATICS
ISSN0862-7940
Volume63Issue:3Pages:281-303
AbstractWe propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.
Keywordeigenvalue problem finite element method Newton's method multilevel iteration
DOI10.21136/AM.2018.0086-18
Language英语
Funding ProjectScience Challenge Project[TZ2016002] ; National Natural Science Foundations of China[NSFC 11771434] ; National Natural Science Foundations of China[91330202] ; National Natural Science Foundations of China[11371026] ; National Natural Science Foundations of China[91430108] ; National Natural Science Foundations of China[11771322] ; National Natural Science Foundations of China[11626033] ; National Natural Science Foundations of China[11601368] ; National Center for Mathematics and Interdisciplinary Science, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000440108200006
PublisherACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30825
Collection计算数学与科学工程计算研究所
Affiliation1.Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
2.Tianjin Univ Finance & Econ, Coordinated Innovat Ctr Computable Modeling Manag, Tianjin 300222, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
5.CAEP Software Ctr High Performance Numer Simulat, Beijing 100088, Peoples R China
Recommended Citation
GB/T 7714
He, Yunhui,Li, Yu,Xie, Hehu,et al. A MULTILEVEL NEWTON'S METHOD FOR EIGENVALUE PROBLEMS[J]. APPLICATIONS OF MATHEMATICS,2018,63(3):281-303.
APA He, Yunhui,Li, Yu,Xie, Hehu,You, Chun'Guang,&Zhang, Ning.(2018).A MULTILEVEL NEWTON'S METHOD FOR EIGENVALUE PROBLEMS.APPLICATIONS OF MATHEMATICS,63(3),281-303.
MLA He, Yunhui,et al."A MULTILEVEL NEWTON'S METHOD FOR EIGENVALUE PROBLEMS".APPLICATIONS OF MATHEMATICS 63.3(2018):281-303.
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