Acceleration of a two-grid method for eigenvalue problems

Authors:
Xiaozhe Hu and Xiaoliang Cheng

Journal:
Math. Comp. **80** (2011), 1287-1301

MSC (2010):
Primary 65L15, 65N15, 65N25, 65N30, 65N55

DOI:
https://doi.org/10.1090/S0025-5718-2011-02458-0

Published electronically:
February 18, 2011

Corrigendum:
Math. Comp. 84 (2015), 2701--2704.

MathSciNet review:
2785459

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a slightly different linear problem on the fine grid, the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Numerical examples are also provided to demonstrate the efficiency of the new method.

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Additional Information

**Xiaozhe Hu**

Affiliation:
Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People’s Republic of China

Email:
huxiaozhezju@gmail.com

**Xiaoliang Cheng**

Affiliation:
Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People’s Republic of China

Email:
xiaoliangcheng@zju.edu.cn

DOI:
https://doi.org/10.1090/S0025-5718-2011-02458-0

Keywords:
Eigenvalue problems,
finite elements,
partial differential equations,
integral equations,
two-grid method.

Received by editor(s):
October 21, 2009

Received by editor(s) in revised form:
June 15, 2010

Published electronically:
February 18, 2011

Additional Notes:
This work was supported in part by National Science Foundation of China (No. 10871179).

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.