A multigrid method for eigenvalue problems based on shifted-inverse power technique

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• 作者：Hongtao Chen ; Yunhui He ; Yu Li ; Hehu Xie
• 关键词：Eigenvalue problem ; Multigrid ; Shifted ; inverse power iteration ; Finite element method ; 65N30 ; 65N25 ; 65L15 ; 65B99
• 刊名：European Journal of Mathematics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：1
• 期：1
• 页码：207-228
• 全文大小：465KB
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• 作者单位：Hongtao Chen (1)
  Yunhui He (2)
  Yu Li (3)
  Hehu Xie (4)
  
  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
  2. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  3. Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin, 300222, China
  4. LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  
• 刊物类别：Algebraic Geometry;
• 刊物主题：Algebraic Geometry;
• 出版者：Springer International Publishing
• ISSN：2199-6768

文摘

A multigrid method is proposed to solve eigenvalue problems by means of the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to solving a series of nonsingular boundary value problems on multilevel meshes. As replacing the difficult eigenvalue solving by an easier solving of boundary value problems, the multigrid way can improve the overall efficiency of the eigenvalue problem solving. Some numerical experiments are presented to validate the efficiency of this new method. Keywords Eigenvalue problem Multigrid Shifted-inverse power iteration Finite element method