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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 529498, 21 pages
Research Article

Highly Efficient Calculation Schemes of Finite-Element Filter Approach for the Eigenvalue Problem of Electric Field

1School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
2School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550004, China

Received 10 October 2012; Accepted 4 December 2012

Academic Editor: Rafael Martinez-Guerra

Copyright © 2012 Yu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper discusses finite-element highly efficient calculation schemes for solving eigenvalue problem of electric field. Multigrid discretization is extended to the filter approach for eigenvalue problem of electric field. With this scheme one solves an eigenvalue problem on a coarse grid just at the first step, and then always solves a linear algebraic system on finer and finer grids. Theoretical analysis and numerical results show that the scheme has high efficiency. Besides, we use interpolation postprocessing technique to improve the accuracy of solutions, and numerical results show that the scheme is an efficient and significant method for eigenvalue problem of electric field.