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A multi-level correction scheme for eigenvalue problems


Authors: Qun Lin and Hehu Xie
Journal: Math. Comp. 84 (2015), 71-88
MSC (2010): Primary 65N30, 65B99; Secondary 65N25, 65L15
DOI: https://doi.org/10.1090/S0025-5718-2014-02825-1
Published electronically: March 10, 2014
MathSciNet review: 3266953
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Abstract: In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by the finite element method. This type of multi-level correction method includes multi correction steps in a sequence of finite element spaces. In each correction step, we only need to solve a source problem on a finer finite element space and an eigenvalue problem on the coarsest finite element space. The accuracy of the eigenpair approximation can be improved after each correction step. This correction scheme can improve the efficiency of solving eigenvalue problems by the finite element method.


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Additional Information

Qun Lin
Affiliation: LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Email: linq@lsec.cc.ac.cn

Hehu Xie
Affiliation: LSEC, ICMSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Email: hhxie@lsec.cc.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-2014-02825-1
Keywords: Eigenvalue problem, multi-level correction scheme, finite element method, multi-space, multi-grid
Received by editor(s): January 23, 2011
Received by editor(s) in revised form: December 20, 2011, October 9, 2012, and April 18, 2013
Published electronically: March 10, 2014
Additional Notes: This work was supported in part by the National Science Foundation of China (NSFC 11001259, 11031006, 11371026, 11201501, 2011CB309703), the Croucher Foundation of the Hong Kong Baptist University and the National Center for Mathematics and Interdisciplinary Science, CAS and the President Foundation of AMSS-CAS
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.