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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 529498, 21 pages
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.
- A. Buffa Jr., P. Ciarlet, and E. Jamelot, “Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements,” Numerische Mathematik, vol. 113, no. 4, pp. 497–518, 2009.
- P. Ciarlet Jr., “Augmented formulations for solving Maxwell equations,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 2-5, pp. 559–586, 2005.
- P. Ciarlet Jr. and G. Hechme, “Computing electromagnetic eigenmodes with continuous Galerkin approximations,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 2, pp. 358–365, 2008.
- M. Costabel and M. Dauge, “Weighted regularization of Maxwell equations in polyhedral domains. A rehabilitation of nodal finite elements,” Numerische Mathematik, vol. 93, no. 2, pp. 239–277, 2002.
- M. Costabel and M. Dauge, “Computation of resonance frequencies for Maxwell equations in non smooth domains,” in Computational Methods for Wave Propagation in Direct Scattering, vol. 31 of Lecture Notes in Computational Science and Engineering, pp. 125–161, Springer, Berlin, Germany, 2003.
- Y. Yang, W. Jiang, Y. Zhang, W. Wang, and H. Bi, “A two-scale discretization scheme for mixed variational formulation of eigenvalue problems,” Abstract and Applied Analysis, vol. 2012, Article ID 812914, 29 pages, 2012.
- Y. Yang, Y. Zhang, and H. Bi, “Multigrid discretization and iterative algorithm for mixed variational formulation of the eigenvalue problem of electric field,” Abstract and Applied Analysis, vol. 2012, Article ID 190768, 25 pages, 2012.
- J. Xu, “A new class of iterative methods for nonselfadjoint or indefinite problems,” SIAM Journal on Numerical Analysis, vol. 29, no. 2, pp. 303–319, 1992.
- J. Xu, “A novel two-grid method for semilinear elliptic equations,” SIAM Journal on Scientific Computing, vol. 15, no. 1, pp. 231–237, 1994.
- J. Xu, “Two-grid discretization techniques for linear and nonlinear PDEs,” SIAM Journal on Numerical Analysis, vol. 33, no. 5, pp. 1759–1777, 1996.
- Y. He, J. Xu, A. Zhou, and J. Li, “Local and parallel finite element algorithms for the Stokes problem,” Numerische Mathematik, vol. 109, no. 3, pp. 415–434, 2008.
- M. Mu and J. Xu, “A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow,” SIAM Journal on Numerical Analysis, vol. 45, no. 5, pp. 1801–1813, 2007.
- C. S. Chien and B. W. Jeng, “A two-grid discretization scheme for semilinear elliptic eigenvalue problems,” SIAM Journal on Scientific Computing, vol. 27, no. 4, pp. 1287–1304, 2006.
- J. Li, “Investigations on two kinds of two-level stabilized finite element methods for the stationary Navier-Stokes equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1470–1481, 2006.
- J. Xu and A. Zhou, “A two-grid discretization scheme for eigenvalue problems,” Mathematics of Computation, vol. 70, no. 233, pp. 17–25, 2001.
- Y. Yang and H. Bi, “Two-grid finite element discretization schemes based on shifted-inverse power method for elliptic eigenvalue problems,” SIAM Journal on Numerical Analysis, vol. 49, no. 4, pp. 1602–1624, 2011.
- H. Bi and Y. Yang, “Multiscale discretization scheme based on the Rayleigh quotient iterative method for the Steklov Eigenvalue problem,” Mathematical Problems in Engineering, vol. 2012, Article ID 487207, 18 pages, 2012.
- Q. Lin and Y. D. Yang, “Interpolation and correction of finite element methods,” Mathematics in Practice and Theory, vol. 3, pp. 29–35, 1991 (Chinese).
- C. Chen and Y. Huang, High Accuracy Theory of Finite Element Methods, Science Press, Changsha, China, 1995.
- Q. Lin and N. Yan, The Construction and Analysis of High Efficient FEM, Hebei University Publishing, Baoding, China, 1996.
- N. Yan, Superconvergence Analysis and a Posteriori Error Estimation in Finite Element Methods, Science Press, Beijing, China, 2008.
- Y. Yang, Finite Element Methods For Eigenvalue Problems, Science Press, Beijing, China, 2012.
- Q. Lin and Q. Zhu, The Preprocessing and Postprocessing for the Finite Element Method, Scientific and Technical Publishers, Shanghai, China, 1994.
- Q. Zhu, Superconvergence and Postprocessing Theory of Finite Elements, Science Press, Beijing, China, 2008.
- Z. Li, H. Huang, and N. Yan, Global Superconvergence of Finite Elements for Elliptic Equations and Its Applications, Science Press, Beijing, China, 2012.
- I. Babuška and J. Osborn, “Eigenvalue problems,” in Finite Element Methods (Part 1), Handbook of Numerical Analysis, P. G. Ciarlet and J. L. Lions, Eds., vol. 2, pp. 640–787, Elsevier Science Publishers, North Holland, The Netherlands, 1991.
- Y. Zhang, W. Wang, and Y. Yang, “Two-grid discretization schemes based on the filter approach for the Maxwell eigenvalue problem,” Procedia Engineering, vol. 37, pp. 143–149, 2012.
- M. Dauge, “Benchmark computations for Maxwell equations for the approximation of highly singular solutions,” http://perso.univ-rennes1.fr/monique.dauge/benchmax.html.
- W. Wang, Y. Zhang, and Y. Yang, “The efficient discretization schemes for the Maxwell eigenvalue problem,” Procedia Engineering, vol. 37, pp. 161–168, 2012.