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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Acceleration of a two-grid method for eigenvalue problems
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by Xiaozhe Hu and Xiaoliang Cheng PDF
Math. Comp. 80 (2011), 1287-1301 Request permission

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
  • 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
  • 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).
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2785459