volume | PIER Journals

Abstract

An efficient and stable hybrid method, based on the time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is developed for investigating transient radiation and scattering from perfectly electrical conducting (PEC) objects. It at first requires partitioning the PEC object surface into TDIE and TDPO regions, respectively. Then, a set of hybrid TDIE-TDPO equations is derived and solved using an adaptive marching-on-in-order (MOO) method. The fast Fourier transforms (FFT)-based blocking scheme is further implemented into the proposed algorithm so as to reduce N²_O dependence of the traditional MOO method to N_Olog²(N_O), where N_O is the highest order of the weighted Laguerre polynomials used for computation. Under such circumstances, its computational cost, in comparison with the full TDIE-MOO solver, is reduced significantly. Several numerical examples are presented to demonstrate its accuracy and efficiency in solving some typical transient electromagnetic problems.

1. Bluck, M. J. and S. P.Walker, "Time-domain BIE analysis of large three dimensional electromagnetic scattering problems," IEEE Trans. on Antennas and Propagat., Vol. 45, No. 5, 894-901, May 1997.
doi:10.1109/8.575643 Google Scholar

2. Wang, X., R. A. Wildman, D. S. Weile, and P. Monk, "A finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics," IEEE Trans. on Antennas and Propagat., Vol. 56, No. 8, Part 1, 2442-2452, Aug. 2008. Google Scholar

3. Andriulli, F. P., K. Cools, F. Olyslager, and E. Michielssen, "Time domain Calderón identities and their application to the integral equation analysis of scattering by PEC objects part II: Stability," IEEE Trans. on Antennas and Propagat., Vol. 57, No. 8, 2365-2375, Aug. 2009.
doi:10.1109/TAP.2009.2024464 Google Scholar

4. Zhang, G.-H., M. Xia, and X.-M. Jiang, "Transient analysis of wire structures using time domain integral equation method with exact matrix elements," Progress In Electromagnetics Research, Vol. 92, 281-298, 2009.
doi:10.2528/PIER09032003 Google Scholar

5. 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 Google Scholar

6. Ji, Z., T. K. Sarkar, B. H. Jung, Y. S. Chung, M. Salazar-Palma, and M. Yuan, "A stable solution of time domain electric ¯eld integral equation for thin-wire antennas using the Laguerre polynomials," IEEE Trans. on Antennas and Propagat., Vol. 52, No. 10, 2641-2649, Oct. 2004.
doi:10.1109/TAP.2004.834437 Google Scholar

7. Jung, B.-H., T. K. Sarkar, and Y.-S. Chung, "Solution of time domain PMCHW formulation for transient electromagnetic scattering from arbitrarily shaped 3-D dielectric objects ," Progress In Electromagnetics Research, Vol. 45, 291-312, 2004.
doi:10.2528/PIER03082502 Google Scholar

8. 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 Google Scholar

9. Xue, M. F. and W. Y. Yin, "Wideband pulse responses of fractal monopole antennas under the impact of an EMP," IEEE Trans. on Electromagn. Compat., Vol. 52, No. 1, 98-107, Feb. 2010.
doi:10.1109/TEMC.2009.2038065 Google Scholar

10. Zhu, M. D., X. L. Zhou, and W. Y. Yin, "An adaptive marching-on-in-order method with FFT-based blocking scheme," IEEE Antennas Wireless Propag. Lett., Vol. 9, 436-439, 2010. Google Scholar

11. Shanker, B., A. A. Ergin, M. Lu, and E. Michielssen, "Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm," IEEE Trans. on Antennas and Propagat., Vol. 51, No. 3, 628-641, Mar. 2003.
doi:10.1109/TAP.2003.809054 Google Scholar

12. Yilmaz, A. E., J. M. Jin, and E. Michielssen, "Time domain adaptive integral method for surface integral equations," IEEE Trans. on Antennas and Propagat., Vol. 52, No. 10, 2692-2708, Oct. 2004.
doi:10.1109/TAP.2004.834399 Google Scholar

13. Yilmaz, A. E., D. S. Weile, B. Shanker, J. M. Jin, and E. Michielssen, "Fast analysis of transient scattering in lossy media," IEEE Antennas Wireless Propag. Lett., Vol. 1, 14-17, 2002.
doi:10.1109/LAWP.2002.802577 Google Scholar

14. Sun, E. Y. and W. V. T. Rusch, "Time-domain physical-optics," IEEE Trans. on Antennas and Propagat., Vol. 42, 9-15, Jan. 1994. Google Scholar

15. Jakobus, U. and F. M. Landstorfer, "Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape," IEEE Trans. on Antennas and Propagat., Vol. 43, No. 2, 162-169, Feb. 1995.
doi:10.1109/8.366378 Google Scholar

16. Hodges, R. E. and Y. Rahmat-Samii, "An iterative current-based hybrid method for complex structures," IEEE Trans. on Antennas and Propagat., Vol. 43, 265-276, Feb. 1997.
doi:10.1109/8.560345 Google Scholar

17. Obelleiro, F., J. M. Taboada, J. L. Rodríguez, J. O. Rubiños, and A. M. Arias, "Hybrid moment-method physical-optics formulation for modeling the electromagnetic behavior of on-board antennas ," Microwave Opt. Technol. Lett., Vol. 27, No. 2, 88-93, Oct. 2000.
doi:10.1002/1098-2760(20001020)27:2<88::AID-MOP3>3.0.CO;2-4 Google Scholar

18. Djordjevic, M. and B. M. Notaroš, "Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces ," IEEE Trans. on Antennas and Propagat., Vol. 53, No. 2, 800-813, Feb. 2005.
doi:10.1109/TAP.2004.841318 Google Scholar

19. Chen, M., Y. Zhang, X. W. Zhao, and C. H. Liang, "Analysis of antenna around NURBS surface with hybrid MoM-PO technique," IEEE Trans. on Antennas and Propagat., Vol. 55, No. 2, 407-413, Feb. 2007.
doi:10.1109/TAP.2006.889814 Google Scholar

20. Walker, S. P. and M. J. Vartiainen, "Hybridization of curvilinear time-domain integral equation and time-domain optical methods for electromagnetic scattering analysis ," IEEE Trans. on Antennas and Propagat., Vol. 46, No. 3, 318-324, Mar. 1998.
doi:10.1109/8.662650 Google Scholar

21. Kobidze, G., B. Shanker, and E. Michielssen, "Hybrid PO-PWTD scheme for analyzing of scattering from electrically large PEC objects," IEEE Antennas and Propagation Society Int. Symp., Vol. 3, 547-555, 2003.

22. Qin, S. T., S. X. Gong, R.Wang, and L. X. Guo, "A TDIE/TDPO hybrid method for the analysis of TM transient scattering from two-dimensional combinative conducting cylinders," Progress In Electromagnetic Research, Vol. 102, 181-195, 2010.
doi:10.2528/PIER09122405 Google Scholar

23. Junker, G. P., A. A. Kishk, and A. W. Glisson, "A novel delta gap source model for center fed cylindrical dipoles," IEEE Trans. on Antennas and Propagat., Vol. 43, No. 5, 537-540, May 1995.
doi:10.1109/8.384200 Google Scholar

24. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. on Antennas and Propagat., Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818 Google Scholar

25. Glassner, A. S., An Introduction to Ray Tracing, Academic Press, 1989.

26. Rius, J. M., M. Ferrando, and L. Jofre, "High-frequency RCS of complex radar targets in real-time," IEEE Trans. on Antennas and Propagat., Vol. 41, No. 9, 1308-1319, Sep. 1993.
doi:10.1109/8.247759 Google Scholar

27. Asvestas, J., "The physical-optics integral and computer graphics," IEEE Trans. on Antennas and Propagat., Vol. 42, No. 12, 1459-1460, Dec. 1995.
doi:10.1109/8.475937 Google Scholar

28. Hairer, E., C. H. Lubich, and M. Schlichte, "Fast numerical solution of nonlinear Volterra convolution equations," SIAM J. Sci. Stat. Comput., Vol. 6, No. 3, 532-541, 1985.
doi:10.1137/0906037 Google Scholar

29. Veruttipong, T. W., "Time domain version of the uniform GTD," IEEE Trans. on Antennas and Propagat., Vol. 38, No. 11, 1757-1764, Nov. 1990.
doi:10.1109/8.102736 Google Scholar

30. Altintas, A. and P. Russer, "Time-domain equivalent edge currents for transient scattering," IEEE Trans. on Antennas and Propagat., Vol. 49, No. 4, 602-606, Apr. 2001.
doi:10.1109/8.923321 Google Scholar

31. Luo, W., W. Y. Yin, M. D. Zhu, and J. Y. Zhao, "Hybrid TDIE-TDPO method for studying on transient responses of some wire and surface structures illuminated by an electromagnetic pulse," Progress In Electromagnetics Research, Vol. 116, 203-219, 2011. Google Scholar

32. Luo, W., W. Y. Yin, M. D. Zhu, and J. F. Mao, "Investigation on electromagnetic responses of some complex wire-surface composite objects using hybrid TDIE-TDPO based MOT method," IEEE Electronmagn. Compat. Symp., 579-584, Aug. 2011. Google Scholar

33. Zhu, M. D., X. L. Zhou, and W. Y. Yin, "Investigation on electromagnetic responses of double objects illuminated by a high-power EMP using hybrid TDIE-TDPO method," IEEE Electronmagn. Compat. Symp., 547-555, Aug. 2010.

34. Zhu, H., Z.-H. Wu, X. Y. Zhang, and B.-J. Hu, "Time-domain integral equation solver for radiation from dipole antenna loaded with general bi-isotropic objects," Progress In Electromagnetics Research B, Vol. 35, 349-367, 2011.
doi:10.2528/PIERB11081907 Google Scholar

35. Guan, Y., S.-X. Gong, S. Zhang, B. Lu, and T. Hong, "A novel time-domain physical optics for computation of electromagnetic scattering of homogeneous dielectric objects," Progress In Electromagnetics Research M, Vol. 14, 123-134, 2010.
doi:10.2528/PIERM10081605 Google Scholar

36. Li, J., B. Wei, Q. He, L.-X. Guo, and D.-B. Ge, "Time-domain terative physical optics method for analysis of EM scattering from the target half buried in rough surface: PEC case," Progress In Electromagnetics Research, Vol. 121, 391-408, 2011.
doi:10.2528/PIER11082906 Google Scholar

Dr. Ming-Da Zhu

Dr. Xi-Lang Zhou

Dr. Wei Luo

Dr. Wen-Yan Yin