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Hamiltonian Analysis and Dual Vector Spectral Elements for 2D Maxwell Eigenproblems

Part of: Numerical problems in dynamical systems Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  07 February 2017

Hongwei Yang ,
Bao Zhu  and
Jiefu Chen
Hongwei Yang*
Affiliation:
College of Applied Sciences, Beijing University of Technology, Beijing 100124, P.R. China
Bao Zhu*
Affiliation:
School of Materials Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R. China
Jiefu Chen*
Affiliation:
Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA
*
*Corresponding author.Email addresses:[email protected] (H. Yang), [email protected] (B. Zhu), [email protected] (J. Chen)
*Corresponding author.Email addresses:[email protected] (H. Yang), [email protected] (B. Zhu), [email protected] (J. Chen)
*Corresponding author.Email addresses:[email protected] (H. Yang), [email protected] (B. Zhu), [email protected] (J. Chen)
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Abstract

The 2D Maxwell eigenproblems are studied from a new point of view. An electromagnetic problem is cast from the Lagrangian system with single variable into the Hamiltonian system with dual variables. The electric and magnetic components transverse to the wave propagation direction are treated as dual variables to each other. Higher order curl-conforming and divergence-conforming vector basis functions are used to construct dual vector spectral elements. Numerical examples demonstrate some unique advantages of the proposed method.

Keywords

Maxwell eigenproblemHamiltonian systemsymplectic eigenvalue analysisdual variablesspectral element method

MSC classification

Secondary: 35Q61: Maxwell equations 65P10: Hamiltonian systems including symplectic integrators 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N25: Eigenvalue problems
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 515 - 525
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, 2014.Google Scholar
[2] Israel, M. and Miniowitz, R., “An efficient finite-element method for nonconvex waveguides based on Hermitian polynomials,” IEEE Trans. Microw. Theory Techn., vol. 35, no. 6, pp. 10191026, Nov. 1987.Google Scholar
[3] Lee, J. F., Sun, D. K., and Cendes, Z. J., “Full-wave analysis of dielectric waveguides using tangential vector finite elements,” IEEE Trans. Microw. Theory Techn., vol. 39, no. 8, pp. 1262–1271, Aug. 1991.CrossRefGoogle Scholar
[4] Zhou, L. Z. and Davis, L. E., “Finite element method with edge elements for waveguides loaded with ferrite magnetized in arbitrary direction,” IEEE Trans. Microw. Theory Techn., vol. 44, no. 6, pp. 809–815, Jun. 1996.Google Scholar
[5] Radhakrishnan, K., and Chew, W. C., “Efficient analysis of waveguiding structures,” Chapter 10, Fast and Efficient Algorithms in Computational Electromagnetics, Chew, W. C., Jin, J. M., Michielssen, E., and Song, J., Artech House, 2001 Google Scholar
[6] Chen, J., Zhu, B., and Zhong, W. X., “Semi-analytical dual edge element method and its application to waveguide discontinuities,” Acta Phys. Sin., vol. 58, no. 2, pp. 1091–1099, Feb. 2009.CrossRefGoogle Scholar
[7] Chen, J., Zhu, B., and Zhong, W. X., “A dual vector spectral element method for waveguide analysis,” IEEE International Conference on Microwave Technology & Computational Electromagnetics, pp. 398–401, Beijing, 2011.Google Scholar
[8] Dai, Q., Chew, W. C., and Jiang, L. J., “Differential forms inspired discretization for finite element analysis of inhomogeneous waveguides,” Prog. Electromagn. Res., vol. 143, pp. 745760, 2013.Google Scholar
[9] Zhong, W. X., Duality System In Applied Mechanics And Optimal Control, Kluwer, 2004.Google Scholar
[10] Garcia-Castillo, L. E., Salazar-Palma, M., and Sarkar, T. K., “Third-order Nédélec curl-conforming finite element,” IEEE Trans. Magn, vol. 38, no. 5, pp. 2370–2372, Sept. 2002.Google Scholar
[11] Lee, J. H., Xiao, T., and Liu, Q. H., “A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 1, pp. 437444, Jan. 2006.Google Scholar
[12] Nédélec, J. C., “Mixed finite elements in ℝ 3 ,” Numer. Math., vol. 35, no. 3, pp. 315–341, Mar. 1980.CrossRefGoogle Scholar
[13] Nédélec, J. C., “A new family of mixed finite elements in ℝ 3 ,” Numer. Math., vol. 50, no. 1, pp. 57–81, Jan. 1986.Google Scholar
[14] Peterson, A. F., Ray, S. L., and Mittra, R., Computational Methods for Electromagnetics, IEEE Press, 1998.Google Scholar
[15] Chen, J., Zhu, B., Zhong, W. X., and Liu, Q. H., “A semianalytical spectral element method for the analysis of 3-D layered structures,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 1, pp. 1–8, Apr. 2011.CrossRefGoogle Scholar