A Cascadic Multigrid Method for Eigenvalue Problem

Authors

  • Xiaole Han IAPCM, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
  • Hehu Xie LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Fei Xu Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China

DOI:

https://doi.org/10.4208/jcm.1608-m2014-0135

Keywords:

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

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.

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Published

2018-08-22

Issue

Vol. 35 No. 1 (2017)

Section

Articles