PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 79 > pp. 339-352

SOLVING TIME DOMAIN HELMHOLTZ WAVE EQUATION WITH MOD-FDM

By B.-H. Jung and T. K. Sarkar

Full Article PDF (145 KB)

Abstract:
In this work, we present a marching-on in degree finite difference method (MOD-FDM) to solve the time domain Helmholtz wave equation. This formulation includes electric and magnetic current densities that are expressed in terms of the incident field for scattering problems for an open region to implement a plane wave excitation. The unknown time domain functional variations for the electric field are approximated by an orthogonal basis function set that is derived using the Laguerre polynomials. These temporal basis functions are also used to expand current densities. With the representation of the derivatives of the time domain variable in an analytic form, all the time derivatives of the field and current density can be handled analytically. By applying a temporal testing procedure, we get a matrix equation that is solved in a marching-on in degree technique as the degree of the temporal basis functions is increased. Numerical results computed using the proposed formulation are presented and compared with the solutions of the conventional time domain finite difference method (TD-FDM) and analytic solutions.

Citation:
B.-H. Jung and T. K. Sarkar, " solving time domain helmholtz wave equation with MOD - FDM ," Progress In Electromagnetics Research, Vol. 79, 339-352, 2008.
doi:10.2528/PIER07102802
http://www.jpier.org/PIER/pier.php?paper=07102802

References:
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 3, 302-307, 1966.
doi:10.1109/TAP.1966.1138693

2. Kunz, K. S. and R. J. Ruebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press, 1993.

3. Taflove, A., Computational Electrodynamics: The Finite- Difference Time-Domain Method, Artech House, 1995.

4. Uduwawala, D., "Modeling and investigation of planar parabolic dipoles for GPR applications: A comparison with bow-tie using FDTD," J. Electromagn. Waves Applicat., Vol. 20, No. 2, 227-236, 2006.
doi:10.1163/156939306775777224

5. Ding, W., Y. Zhang, P. Y. Zhu, and C. H. Liang, "Study on electromagnetic problems involving combinations of arbitrarily oriented thin-wire antennas and inhomogeneous dielectric objects with a hybrid MoM-FDTD method," J. Electromagn. Waves Applicat., Vol. 20, No. 11, 1519-1533, 2006.
doi:10.1163/156939306779274255

6. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3-D buried objects using parallel genetic algorithm combined with FDTD technique," J. Electromagn. Waves Applicat., Vol. 20, No. 13, 1761-1774, 2006.
doi:10.1163/156939306779292264

7. Chen, Z. H. and Q. X. Chu, "FDTD modeling of arbitrary linear lumped networks using piecewise linear recursive convolution technique," Progress In Electromagnetics Research, Vol. 73, 327-341, 2007.
doi:10.2528/PIER07042002

8. Chung, Y. S., T. K. Sarkar, B. H. Jung, and M. Salazar-Palma, "An unconditionally stable scheme for the finite-difference timedomain method," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 3, 697-704, 2003.
doi:10.1109/TMTT.2003.808732

9. Jung, B. H., Y.-S. Chung, and T. K. Sarkar, "Time-domain EFIE, MFIE, and CFIE formulations using Laguerre polynomials as temporal basis functions for the analysis of transient scattering from arbitrary shaped conducting structures," Progress In Electromagnetics Research, Vol. 39, 1-45, 2003.
doi:10.2528/PIER02083001

10. Jung, B. H., T. K. Sarkar, and M. Salazar-Palma, "Time domain EFIE and MFIE formulations for analysis of transient electromagnetic scattering from 3-D dielectric objects," Progress In Electromagnetics Research, Vol. 49, 113-142, 2004.
doi:10.2528/PIER04022304

11. Jung, B. H., Z. Ji, T. K. Sarkar, M. Salazar-Palma, and M. Yuan, "A comparison of marching-on in time method with marching-on in degree method for the TDIE solver," Progress In Electromagnetics Research, Vol. 70, 281-296, 2007.
doi:10.2528/PIER07013002

12. Chung, Y.-S., T. K. Sarkar, S. Llorento-Romano, and M. Salazar- Palma, "Finite element time domain method using Laguerre polynomials," 2003 IEEE MTT-S Int. Microwave Symp. Digest, Vol. 2, No. 6, 981-984, 2003.
doi:10.1109/MWSYM.2003.1212533

13. Shao, W., B.-Z. Wang, and Z.-J. Yu, "Space-domain finite difference and time-domain moment method for electromagnetic simulation," IEEE Trans. Electromagn. Compat., Vol. 48, No. 1, 10-18, 2006.
doi:10.1109/TEMC.2005.861376

14. Ding, P.-P., G. Wang, H. Lin, and B.-Z. Wang, "Unconditionally stable FDTD formulation with UPML-ABC," IEEE Microw. Wireless Compon. Lett., Vol. 16, No. 4, 161-163, 2006.
doi:10.1109/LMWC.2006.872147

15. Shao, W., B.-Z. Wang, and X.-F. Liu, "Second-order absorbing boundary conditions for marching-on-in-order scheme," IEEE Microw. Wireless Compon. Lett., Vol. 16, No. 5, 308-310, 2006.
doi:10.1109/LMWC.2006.873480

16. Shao, W., B.-Z. Wang, X.-H. Wang, and X.-F. Liu, "Efficient compact 2-D time-domain method with weighted Laguerre polynomials," IEEE Trans. Electromagn. Compat., Vol. 48, No. 3, 442-448, 2006.
doi:10.1109/TEMC.2006.879332

17. Alighanbari, A. and C. D. Sarris, "An unconditionally stable Laguerre-based S-MRTD time-domain scheme," IEEE Antennas Wireless Propag. Lett., Vol. 5, 69-72, 2006.
doi:10.1109/LAWP.2006.870364

18. Yi, Y., B. Chen, H.-L. Chen, and D.-G. Fang, "TF/SF boundary and PML-ABC for an unconditionally stable FDTD method," IEEE Microw. Wireless Compon. Lett., Vol. 17, No. 2, 91-93, 2007.
doi:10.1109/LMWC.2006.890324

19. Shao, W., B. Z. Wang, and X. F. Liu, "Complex variable technique in compact 2-D order-marching time-domain method," J. Electromagn. Waves Applicat., Vol. 21, No. 11, 1453-1460, 2007.

20. Jung, B. H. and T. K. Sarkar, "Analysis of transient electromagnetic scattering with plane wave incidence using MODFDM," Progress In Electromagnetics Research, Vol. 77, 111-120, 2007.
doi:10.2528/PIER07080302

21. Jordan, E. C. and K. G. Balmain, Electromagnetic Waves and Radiating Systems, 2nd edition, Chap. 5, Prentice-Hall, Inc., 1968.

22. Aoyagi, P. H., J.-F. Lee, and R. Mittra, "A hybrid Yee algorithm/scalar-wave equation approach," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 9, 1593-1600, 1993.
doi:10.1109/22.245683

23. Maloney, J. G. and G. S. Smith, "Modeling of antennas," Advances in Computational Electrodynamics: The Finite-Difference Time- Domain Method, 1998.

24. Poularikas, A. D., The Transforms and Applications Handbook, 2nd edition, CRC Press, 2000.

25. Yuan, M., A. De, T. K. Sarkar, J. Koh, and B. H. Jung, "Conditions for generation of stable and accurate hybrid TD-FD MoM solutions," IEEE Trans. Microwave Theory Tech., Vol. 54, No. 6, 2552-2563, 2006.
doi:10.1109/TMTT.2006.875823

26. Rao, S. M., Time Domain Electromagnetics, Academic Press, 1999.

27. Kong, J. A., Electromagnetic Wave Theory, 2nd edition, Chap. 3, John Wiley & Sons, Inc., 1990.


© Copyright 2014 EMW Publishing. All Rights Reserved