To improve stability of time-domain integral equation, a stable implicit scheme is proposed to solve the transverse-magnetic (TM) electromagnetic scattering from 2D conducting objects. The time-domain electric-field integral equation (TD-EFIE) was adopted and expressed using second-order derivative of the magnetic vector potential. To reduce numerical error, the magnetic vector potential was approximated by second-order central finite difference. TM transient scattering from 2D conducting objects was calculated by an implicit marching-on-in-time (MOT) scheme. To obtain stable numerical results, the TD-EFIE MOT implicit scheme was firstly combined with the time-averaging technique. The accuracy and stability of the scheme were demonstrated by comparison with the results from inverse discrete Fourier transform technique.
2. Xiao, G., X. Tian, W. Luo, and J. Fang, "Impulse responses and the late time stability properties of time-domain integral equations," IET Microw. Antennas Propag., Vol. 9, No. 7, 603-610, 2014.
3. Jung, B. H., T. K. Sarkar, Y. S. Chung, M. S. Palma, Z. Ji, S. M. Jang, and K. J. Kim, "Transient electromagnetic scattering from dielectric objects using the electric field integral equation with Laguerre polynomials as temporal basis functions," IEEE Trans. Antennas Propag., Vol. 52, No. 9, 2329-2340, 2004.
4. 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.
5. He, Z. and R. S. Chen, "A novel marching-on-in-degree solver of time domain parabolic equation for transient EM scattering analysis," IEEE Trans. Antennas Propag., Vol. 64, No. 11, 4905-4910, 2016.
6. Ergin, A., B. Shanker, and E. Michielssen, "Fast evaluation of three-dimensional transient wave field using diagonal translation operators," J. Comput. Phys., Vol. 146, No. 1, 157-180, 1998.
7. Yilmaz, E., D. S. Weile, J. M. Jin, and E. Michielssen, "A hierarchical FFT algorithm (HIL-FFT) for the fast analysis of transient electromagnetic scattering phenomena," IEEE Trans. Antennas Propag., Vol. 50, No. 7, 971-982, 2002.
8. Vechinski, D. A. and S. M. Rao, "A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 40, No. 6, 661-665, 1993.
9. Rao, S. M., D. A. Vechinski, and T. K. Sarkar, "Transient scattering by conducting cylinders — Implicit solution for the transverse electric case," Microw. Opt. Technol. Lett., Vol. 21, No. 2, 129-134, 1999.
\10. Guo, X. Y., M. Y. Xia, and C. H. Chan, "Stable TDIE-MOT solver for transient scattering by two-dimensional conducting structures," IEEE Trans. Antennas Propag., Vol. 62, No. 4, 2149-2455, 2014.
11. Tong, M. S. and P. C. Wang, "Stable solution of time-domain combined field integral equations for transient electromagnetic scattering by composite structures based on Nystr¨om scheme and laguerre function," IEEE Trans. Antennas Propag., Vol. 64, No. 7, 3239-3244, 2016.
12. Rao, S. M. and T. K. Sarkar, "An alternative version of the time-domain electric field integral equation for arbitrarily shaped conductors," IEEE Trans. Antennas Propag., Vol. 41, No. 6, 831-834, 1993.
13. Davies, P. J., "On the stability of time-marching schemes for the general surface electric-field integral equation," IEEE Trans. Antennas Propag., Vol. 44, No. 11, 1467-1473, 2002.
14. Jung, H. and T. K. Sarkar, "Time-domain CFIE for the analysis of transient scattering from arbitrarily shaped 3D conducting objects," Microw. Opt. Technol. Lett., Vol. 34, No. 4, 289-296, 2002.
15. Rao, S. M. and D. R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 39, No. 1, 56-61, 1991.
16. Guan, X. P., Y. Su, and S. G. Wang, "Stable and accelerated procedure to calculate transient scattering using electric field integral equation," IEE Electron. Lett., Vol. 43, No. 15, 794-795, 2007.