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2013-03-04
Elimination of Numerical Dispersion from Electromagnetic Time Domain Analysis by Using Resource Efficient Finite Element Technique
By
Progress In Electromagnetics Research, Vol. 137, 487-512, 2013
Abstract
Time domain analysis of electromagnetic wave propagation is required for design and characterization of many optical and microwave devices. The FDTD method is one of the most widely used time domain methods for analysing electromagnetic scattering and radiation problems. However, due to the use of the Finite Difference grid, this method suffers from higher numerical dispersion and inaccurate discretisation due to staircasing at slanted and curve edges. The Finite Element (FE)-based meshing technique can discretize the computational domain offering a better approximation even when using a small number of elements. Some of the FE-based approaches have considered either an implicit solution, higher order elements, the solution of a large matrix or matrix lumping, all of which require more time and memory to solve the same problem or reduce the accuracy. This paper presents a new FE-based method which uses a perforated mesh system to solve Maxwell's equations with linear elements. The perforated mesh reduces the requirement on memory and computational time to less than half of that compared to other FE-based methods. This paper also shows a very large improvement in the numerical dispersion over the FDTD method when the proposed method is used with an equilateral triangular mesh.
Citation
S M Raiyan Kabir B. M. Azizur Rahman Arti Agrawal Ken Thomas Victor Grattan , "Elimination of Numerical Dispersion from Electromagnetic Time Domain Analysis by Using Resource Efficient Finite Element Technique," Progress In Electromagnetics Research, Vol. 137, 487-512, 2013.
doi:10.2528/PIER13012305
http://www.jpier.org/PIER/pier.php?paper=13012305
References

1. Yee, K., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, 302-307, 1966.

2. Taflove, A. and S. Hagness, Computational Electrodynamics, Artech House, Boston, 1995.

3. Taflove, A. and M. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Transactions on Microwave Theory and Techniques, Vol. 23, No. 8, 623-630, 1975.
doi:10.1109/TMTT.1975.1128640

4. Sun, G. and C. Trueman, "Some fundamental characteristics of the one-dimensional alternate-direction-implicit finite-difference time-domain method," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 1, 46-52, 2004.
doi:10.1109/TMTT.2003.821230

5. Lee, J., R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 3, 430-442, 1997.
doi:10.1109/8.558658

6. Guiffaut, C. and K. Mahdjoubi, "A parallel FDTD algorithm using the MPI library," IEEE Antennas and Propagation Magazine, Vol. 43, No. 2, 94-103, 2001.
doi:10.1109/74.924608

7. Adams, S., J. Payne, and R. Boppana, "Finite difference time domain (FDTD) simulations using graphics processors," IEEE DoD High Performance Computing Modernization Program Users Group Conference, 334-338, 2007.
doi:10.1109/HPCMP-UGC.2007.34

8. Sypek, P., A. Dziekonski, and M. Mrozowski, "How to render FDTD computations more effective using a graphics accelerator," IEEE Transactions on Magnetics, Vol. 45, No. 3, 1324-1327, 2009.
doi:10.1109/TMAG.2009.2012614

9. Smyk, A. and M. Tudruj, "Openmp/MPI programming in a multi-cluster system based on shared memory/message passing communication," Advanced Environments, Tools, and Applications for Cluster Computing, 157-160, 2002.

10. Farjadpour, A., D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. Joannopoulos, S. Johnson, and G. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Optics Letters, Vol. 31, No. 20, 2972-2974, 2006.
doi:10.1364/OL.31.002972

11. Rahman, B. M. A. and J. Davies, "Finite-element analysis of optical and microwave waveguide problems," IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 1, 20-28, 1984.
doi:10.1109/TMTT.1984.1132606

12. Rahman, B. M. A. and J. Davies, "Finite-element solution of integrated optical waveguides," Journal of Lightwave Technology, Vol. 2, No. 5, 682-688, 1984.
doi:10.1109/JLT.1984.1073669

13. Hayata, K., M. Koshiba, M. Eguchi, and M. Suzuki, "Vectorial finite-element method without any spurious solutions for dielectric waveguiding problems using transverse magnetic-field component," IEEE Transactions on Microwave Theory and Techniques, Vol. 34, No. 11, 1120-1124, 1986.
doi:10.1109/TMTT.1986.1133508

14. Cangellaris, A., C. Lin, and K. Mei, "Point-matched time domain finite element methods for electromagnetic radiation and scattering," IEEE Transactions on Antennas and Propagation, Vol. 35, No. 10, 1160-1173, 1987.
doi:10.1109/TAP.1987.1143981

15. Feliziani, M. and E. Maradei, "Point matched finite element-time domain method using vector elements," IEEE Transactions on Magnetics, Vol. 30, No. 5, 3184-3187, 1994.
doi:10.1109/20.312614

16. Koshiba, M., Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," Journal of Lightwave Technology, Vol. 18, No. 1, 102, 2000.
doi:10.1109/50.818913

17. Hesthaven, T. W. J. S., "High-order/spectral methods on un-structured grids I. Time-domain solution of Maxwell's equations ,", Tech. Rep. 2001-6-ICASE NASA Langley Research Center, Hampton, Virginia, March 2001.

18. Songoro, H., M. Vogel, and Z. Cendes, "Keeping time with Maxwell's equations," IEEE Microwave Magazine, Vol. 11, No. 2, 42-49, 2010.
doi:10.1109/MMM.2010.935779

19. Gedney, S. and U. Navsariwala, "An unconditionally stable finite element time-domain solution of the vector wave equation," IEEE Microwave and Guided Wave Letters, Vol. 5, No. 10, 332-334, 1995.
doi:10.1109/75.465046

20. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition, Princeton University Press, 2008.

21. Berenger, J., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, No. 2, 185-200, 1994.
doi:10.1006/jcph.1994.1159

22. Berenger, J., "Perfectly matched layer for the fdtd solution of wave-structure interaction problems," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 1, 110-117, 1996.
doi:10.1109/8.477535

23. Veselago, V., et al., "The electrodynamics of substances with simultaneously negative values of ε and μ," Physics-Uspekhi, Vol. 10, No. 4, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

24. Hao, Y. and R. Mittra, FDTD Modeling of Metamaterials, Artech House, 2009.

25. Juntunen, J. and T. Tsiboukis, "Reduction of numerical dispersion in FDTD method through artificial anisotropy," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 4, 582-588, 2000.
doi:10.1109/22.842030

26. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd edition, Artech House, 2000.