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Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem

Published online by Cambridge University Press:  23 January 2015

Na Liu ,
Luis Tobón ,
Yifa Tang  and
Qing Huo Liu
Na Liu
Affiliation:
Institute of Electromagnetics and Acoustics, Xiamen University, Xiamen, 361005, P.R. China
Luis Tobón
Affiliation:
Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA Departamento de Ciencias e Ingeniería de la Computación, Pontificia Universidad Javeriana, Cali, Colombia
Yifa Tang
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China
Qing Huo Liu*
Affiliation:
Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA
*
*Email addresses: liuna@xmu.edu.cn (N. Liu), let12@duke.edu (L. Tobón), tyf@lsec.cc.ac.cn (Y. Tang), qhliu@duke.edu (Q. H. Liu)
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Abstract

It is well known that conventional edge elements in solving vector Maxwell's eigenvalue equations by the finite element method will lead to the presence of spurious zero eigenvalues. This problem has been addressed for the first order edge element by Kikuchi by the mixed element method. Inspired by this approach, this paper describes a higher order mixed spectral element method (mixed SEM) for the computation of two-dimensional vector eigenvalue problem of Maxwell's equations. It utilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-element framework with a weak divergence condition. It is shown that this method can suppress all spurious zero and nonzero modes and has spectral accuracy. A rigorous analysis of the convergence of the mixed SEM is presented, based on the higher order edge element interpolation error estimates, which fully confirms the robustness of our method. Numerical results are given for homogeneous, inhomogeneous, L-shape, coaxial and dual-inner-conductor cavities to verify the merits of the proposed method.

Keywords

78M1078M22Maxwell eigenvaluesspectral element methodspurious eigenvalues
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 458 - 486
Copyright
Copyright © Global Science Press Limited 2015 

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