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Progress In Electromagnetics Research
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A NON-SPURIOUS VECTOR SPECTRAL ELEMENT METHOD FOR MAXWELL'S EQUATIONS

By J. Chen and Q. H. Liu

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Abstract:
In this paper, a non-spurious vector spectral element method is proposed to solve Maxwell's equations using E and H as variables. The mixed-order curl-conforming basis functions are used for both variables to facilitate applying boundary and interface conditions; and the interpolation degree of basis functions for E is set different from that for H to suppress the spurious modes. The proposed method can be utilized in both time domain and frequency domain, and it is very suitable for the future implementation of discontinuous Galerkin spectral element method. Numerical results demonstrate the property of spurious-free and the spectral accuracy of this method. The method has also been implemented for the more general finite element method in time and frequency domains.

Citation:
J. Chen and Q. H. Liu, "A Non-Spurious Vector Spectral Element Method for Maxwell's Equations," Progress In Electromagnetics Research, Vol. 96, 205-215, 2009.
doi:10.2528/PIER09082705
http://www.jpier.org/PIER/pier.php?paper=09082705

References:
1. Rasetarinera, P. and M. Y. Hussaini, "An efficient implicit discontinuous spectral Galerkin method," J. Comput. Phys., Vol. 172, No. 2, 718-738, Sep. 2001.
doi:10.1006/jcph.2001.6853

2. Kopriva, D. A., S. L. Woodruff, and M. Y. Hussaini, "Computation of electromagnetic scattering with a non-conforming discontinuous spectral element method," Int. J. Numer. Meth. Eng., Vol. 53, No. 1, 105-122, Oct. 2001.
doi:10.1002/nme.394

3. Giraldo, F. X., J. S. Hesthaven, and T. Warburton, "Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations," J. Comput. Phy., Vol. 181, No. 2, 499-525, Sep. 2002.
doi:10.1006/jcph.2002.7139

4. Hesthaven, J. S. and T. C.Warburton, "Nodal high-order methods on unstructured grids --- 1. Time-domain solution of Maxwell's equations," J. Comput. Phys., Vol. 181, 186-221, 2002.
doi:10.1006/jcph.2002.7118

5. Xiao, T. and Q. H. Liu, "Three-dimensional unstructured-grid discontinuous Galerkin method for Maxwell's equations with well-posed perfectly matched layer," Microwave Opt. Technol. Lett., Vol. 46, No. 5, 459-463, 2005.
doi:10.1002/mop.21016

6. Liu, Q. H. and G. Zhao, "Advances in PSTD techniques," Computational Electrodynamics: The Finite-difference Time-domain Method, A. Ta┬░ove and S. Hagness (eds.), Chapter 17, Artech House, Inc., 2005.

7. Shi, Y. and C.-H. Liang, "Simulations of the left-handed medium using discontinuous Galerkin method based on the hybrid domain," Progress In Electromagnetics Research, PIER 63, 171-191, 2006.

8. Kirsch, A. and P. Monk, "A finite element/spectral method for approximating the time-harmonic Maxwell system in R3," SIAM Journal on Applied Mathematics, Vol. 55, No. 5, 1324-1344, Oct. 1995.
doi:10.1137/S0036139993259891

9. Pingenot, J., R. N. Rieben, D. A. White, and D. G. Dudley, "Full wave analysis of RF signal attenuation in a lossy rough surface cave using a high order time domain vector nite element method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1695-1705, 2006.
doi:10.1163/156939306779292408

10. Cohen, G., Higher-order Numerical Methods for Transient Wave Equations, Springer, Berlin, 2002.

11. Lee, J. H., T. Xiao, and Q. H. Liu, "A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 1, 437-444, Jan. 2006.
doi:10.1109/TMTT.2006.886157

12. Lee, J. H. and Q. H. Liu, "A 3-D spectral-element time-domain method for electromagnetic simulation," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 5, 983-991, May 2007.
doi:10.1109/TMTT.2007.895398

13. Mohammadian, A. H., V. Shankar, and W. F. Hall, "Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure," Computer Physics Communications, Vol. 68, No. 1-3, 175-196, Nov. 1991.
doi:10.1016/0010-4655(91)90199-U

14. Nedelec, J. C., "Mixed finite elements in R3," Numerische Mathematik, Vol. 35, No. 3, 315-341, 1980.
doi:10.1007/BF01396415

15. Cohen, G. and M. Durufle, "Non spurious spectral-like element methods for Maxwell's equations," J. Comput. Math., Vol. 25, No. 3, 282-300, 2007.

16. Wang, X. and K. Bathe, "Displacement/pressure based mixed nite element formulations for acoustic UID-structure interaction problems," Intl. J. Numer. Method. Eng., Vol. 40, No. 11, 2001-2017, 1997.
doi:10.1002/(SICI)1097-0207(19970615)40:11<2001::AID-NME152>3.0.CO;2-W

17. Liu, Q. H., "The PSTD algorithm: A time-domain method requiring only two cells per wavelength," Microwave Opt. Technol. Lett., Vol. 15, No. 3, 158-165, Jun. 1997.
doi:10.1002/(SICI)1098-2760(19970620)15:3<158::AID-MOP11>3.0.CO;2-3

18., Wavenology EM User's Manual, Wave Computation Technologies, Inc., 2009.


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