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 N2O dependence of the traditional MOO method to NOlog2(NO), where NO 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
27. Asvestas, J., "The physical-optics integral and computer graphics," IEEE Trans. on Antennas and Propagat., Vol. 42, No. 12, 1459-1460, Dec. 1995.
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.
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.
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.
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.
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.
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.
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.
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.