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Abstract and Applied Analysis
Volume 2012, Article ID 190768, 25 pages
Research Article

Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field

School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received 9 July 2012; Revised 4 September 2012; Accepted 12 September 2012

Academic Editor: Xinan Hao

Copyright © 2012 Yidu Yang 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 highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.