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Volume 35, Issue 1
A Cascadic Multigrid Method for Eigenvalue Problem

Xiaole Han, Hehu Xie & Fei Xu

DOI: 10.4208/jcm.1608-m2014-0135

J. Comp. Math., 35 (2017), pp. 74-90.

Published online: 2017-02

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  • Abstract

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

  • Keywords

Eigenvalue problem, Cascadic multigrid, Multilevel correction scheme, Finite element method.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hanxiaole@lsec.cc.ac.cn (Xiaole Han)

hhxie@lsec.cc.ac.cn (Hehu Xie)

xufei@lsec.cc.ac.cn (Fei Xu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-74, author = {Han , XiaoleXie , Hehu and Xu , Fei}, title = {A Cascadic Multigrid Method for Eigenvalue Problem}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {1}, pages = {74--90}, abstract = {

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1608-m2014-0135}, url = {http://global-sci.org/intro/article_detail/jcm/9764.html} }
TY - JOUR T1 - A Cascadic Multigrid Method for Eigenvalue Problem AU - Han , Xiaole AU - Xie , Hehu AU - Xu , Fei JO - Journal of Computational Mathematics VL - 1 SP - 74 EP - 90 PY - 2017 DA - 2017/02 SN - 35 DO - http://doi.org/10.4208/jcm.1608-m2014-0135 UR - https://global-sci.org/intro/article_detail/jcm/9764.html KW - Eigenvalue problem, Cascadic multigrid, Multilevel correction scheme, Finite element method. AB -

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

Xiaole Han, Hehu Xie & Fei Xu. (2019). A Cascadic Multigrid Method for Eigenvalue Problem. Journal of Computational Mathematics. 35 (1). 74-90. doi:10.4208/jcm.1608-m2014-0135
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