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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
Published electronically: February 18, 2011
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
MR Author ID: 793307

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

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.