Close Search Advanced
Journals
Resources
About Us
Open Access

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

Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem
Preview
Add to basket

Year:    2015

Author:    Na Liu, Luis Tobón, Yifa Tang, Qing Huo Liu

Communications in Computational Physics, Vol. 17 (2015), Iss. 2 : pp. 458–486

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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.230113.140814a

Communications in Computational Physics, Vol. 17 (2015), Iss. 2 : pp. 458–486

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:   

Author Details

Na Liu

Luis Tobón

Yifa Tang

Qing Huo Liu

  1. A posteriori error estimator for mixed interior penalty discontinuous Galerkin finite element method for the H(curl)-elliptic problems

    Tang, Ming | Xing, Xiaoqing | Zhong, Liuqiang

    Journal of Computational and Applied Mathematics, Vol. 436 (2024), Iss. P.115407

    https://doi.org/10.1016/j.cam.2023.115407 [Citations: 0]

  2. The Mixed Finite-Element Method With Mass Lumping for Computing Optical Waveguide Modes

    Liu, Na | Cai, Guoxiong | Zhu, Chunhui | Huang, Yueqin | Liu, Qing Huo

    IEEE Journal of Selected Topics in Quantum Electronics, Vol. 22 (2016), Iss. 2 P.187

    https://doi.org/10.1109/JSTQE.2015.2473689 [Citations: 15]

  3. A hybrid implicit-explicit discontinuous Galerkin spectral element time domain (DG-SETD) method for computational elastodynamics

    Liu, Qi Qiang | Zhuang, Mingwei | Zhan, Weichen | Shi, Linlin | Liu, Qing Huo

    Geophysical Journal International, Vol. 234 (2023), Iss. 3 P.1855

    https://doi.org/10.1093/gji/ggad168 [Citations: 2]

  4. Spectral element method for band-structure calculations of 3D phononic crystals

    Shi, Linlin | Liu, Na | Zhou, Jianyang | Zhou, Yuanguo | Wang, Jiamin | Liu, Qing Huo

    Journal of Physics D: Applied Physics, Vol. 49 (2016), Iss. 45 P.455102

    https://doi.org/10.1088/0022-3727/49/45/455102 [Citations: 21]

  5. The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides

    Liu, Na | Cai, Guoxiong | Zhu, Chunhui | Tang, Yifa | Liu, Qing Huo

    IEEE Transactions on Microwave Theory and Techniques, Vol. 63 (2015), Iss. 10 P.3094

    https://doi.org/10.1109/TMTT.2015.2472416 [Citations: 28]

  6. Convergence of adaptive mixed interior penalty discontinuous Galerkin methods for H(curl)-elliptic problems

    Liu, Kai | Tang, Ming | Xing, Xiaoqing | Zhong, Liuqiang

    Computers & Mathematics with Applications, Vol. 170 (2024), Iss. P.84

    https://doi.org/10.1016/j.camwa.2024.06.020 [Citations: 0]

  7. New Mixed SETD and FETD Methods to Overcome the Low-Frequency Breakdown Problems by Tree-Cotree Splitting

    Chen, Ke | Liu, Jie | Zhuang, Mingwei | Sun, Qingtao | Liu, Qing Huo

    IEEE Transactions on Microwave Theory and Techniques, Vol. 68 (2020), Iss. 8 P.3219

    https://doi.org/10.1109/TMTT.2020.2995721 [Citations: 12]

  8. An Effective Finite Element Method for Maxwell Eigenvalue Problem in a Radial Inhomogeneous Medium

    Wang, Wei | Zheng, Jihui | Han, Jiayu

    2024 Photonics & Electromagnetics Research Symposium (PIERS), (2024), P.1

    https://doi.org/10.1109/PIERS62282.2024.10618840 [Citations: 0]

  9. Domain decomposition based on the spectral element method for frequency-domain computational elastodynamics

    Shi, Linlin | Zhuang, Mingwei | Zhou, Yuanguo | Liu, Na | Liu, Qinghuo

    Science China Earth Sciences, Vol. 64 (2021), Iss. 3 P.388

    https://doi.org/10.1007/s11430-020-9696-4 [Citations: 2]

  10. An efficient decoupled and dimension reduction scheme for quad-curl eigenvalue problem in balls and spherical shells

    Jiang, Jiantao | Zhang, Zhimin

    Computers & Mathematics with Applications, Vol. 174 (2024), Iss. P.454

    https://doi.org/10.1016/j.camwa.2024.10.010 [Citations: 0]

  11. Spectral Element Method and Domain Decomposition for Low-Frequency Subsurface EM Simulation

    Zhou, Yuanguo | Shi, Linlin | Liu, Na | Zhu, Chunhui | Liu, Hai | Liu, Qing Huo

    IEEE Geoscience and Remote Sensing Letters, Vol. 13 (2016), Iss. 4 P.550

    https://doi.org/10.1109/LGRS.2016.2524558 [Citations: 27]

  12. Numerical approximation based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem

    Jiang, Jiantao | An, Jing

    Mathematical Methods in the Applied Sciences, Vol. 46 (2023), Iss. 16 P.17367

    https://doi.org/10.1002/mma.9504 [Citations: 2]

  13. Spectral element method for elastic and acoustic waves in frequency domain

    Shi, Linlin | Zhou, Yuanguo | Wang, Jia-Min | Zhuang, Mingwei | Liu, Na | Liu, Qing Huo

    Journal of Computational Physics, Vol. 327 (2016), Iss. P.19

    https://doi.org/10.1016/j.jcp.2016.09.036 [Citations: 29]

  14. An Efficient Mixed Finite-Element Time-Domain Method for Complex Electrically Small Problems

    Chen, Ke | Hou, Xuanying | Zhuang, Mingwei | Liu, Na | Liu, Qing Huo

    IEEE Transactions on Microwave Theory and Techniques, Vol. 67 (2019), Iss. 4 P.1285

    https://doi.org/10.1109/TMTT.2019.2899842 [Citations: 12]

  15. A Two-Grid Vector Discretization Scheme for the Resonant Cavity Problem With Anisotropic Media

    Liu, Jie | Jiang, Wei | Lin, Fubiao | Liu, Na | Liu, Qing Huo

    IEEE Transactions on Microwave Theory and Techniques, Vol. 65 (2017), Iss. 8 P.2719

    https://doi.org/10.1109/TMTT.2017.2672545 [Citations: 15]

  16. A Hybrid SESI Method for Electromagnetic Scattering by Objects in Multiregion Cylindrically Layered Media

    Guan, Zhen | Liu, Jie | Zhuang, Mingwei | Liu, Qing Huo

    IEEE Transactions on Microwave Theory and Techniques, Vol. 69 (2021), Iss. 9 P.3967

    https://doi.org/10.1109/TMTT.2021.3089821 [Citations: 11]