In this paper, different causal sub-domain temporal basis functions are investigated to make the explicit marching-on-in time schemes converge and stable for solving two dimensional time domain EFIE. PEC cylinders with arbitrary cross section are illuminated by a TE-polarized Gaussian plane wave. Two different approximations are used for calculation of the singular elements of the impedance matrix analytically. In the Time Domain Method of Moment (TD-MoM) formulation of the Electric Field Integral Equation (EFIE) of the problem, the free-space two-dimensional Green's function and triangular spatial basis function are used. By employing Galerkin's method in spatial domain and point matching in time domain, all time convolution integrals and self-terms are evaluated analytically to increase the accuracy and stability of the proposed technique. The stability and efficiency of the new technique are confirmed by comparison with literature.
2. Zhang, G. H., M. Y. 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.
3. Bennett, C. L. and W. L. Weeks, "Transient scattering from conducting cylinders," IEEE Trans. Antennas Propagat., Vol. 18, No. 5, 627-633, 1970.
4. Rao, S. M., D. A. Vechinski, and T. K. Sarkar, "Transient scattering by conducting cylinders --- Implicit solution for the transverse electric case ," Microwave and Opt. Tech. Lett., Vol. 21, No. 2, 129-134, 1999.
5. Geranmayeh, A., W. Ackermann, and T. Weiland, "Temporal discretization choices for stable boundary element method in electromagnetic scattering problems," Applied Numerical Mathematics, Vol. 59, No. 11, 2751-2773, 2009.
6. Rynne, B. P. and P. D. Smith, "Stability of time marching algorithms for the electric field integral equation," Journal of Electromagnetic Waves and Applications, Vol. 4, No. 12, 1181-1205, Dec. 1990.
7. 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, No. 1, 45, 2003.
8. Ding, J., C. Gu, Z. Li, and Z. Niu, "Analysis of transient electromagnetic scattering using time domain fast dipole method," Progress In Electromagnetics Research, Vol. 136, 543-559, 2013.
9. Ding, J., L. Yu, W. Xu, C. Gu, and Z. Li, "Analysis of transient electromagnetic scattering using the multilevel dipole method," Progress In Electromagnetics Research, Vol. 140, 401-413, 2013.
10. 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 Electromagnetics Research, Vol. 102, 181-195, 2010.
11. Geranmayeh, A., W. Ackermann, and T. Weiland, "Proper combination of integrators and interpolators for stable marching-on-in time schemes," Proc. 10th Int. Conf. on Electromagnetics in Advance Applications (ICEAA' 07), 948-951, Torino, Italy, 2007.
12. Firouzeh, Z. H., R. Moini, S. H. H. Sadeghi, R. Faraji-Dana, and G. A. E. Vandenbosch, "A new robust technique for transient analysis of conducting cylinders --- TM case," 5th European Conference on Antennas and Propagation, EuCAP 2011, 1353-1356, Rome, Italy, Apr. 11-15, 2011.
13. Wang, P., M. Y. Xia, J. M. Jin, and L. Z. Zhou, "Time domain integral equation solvers using quadratic B-Spline temporal basis functions," Microwave and Optical Technology Letters, Vol. 49, No. 5, 1154-1159, 2007.
14. Glisson, A. W. and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propagat., Vol. 28, No. 5, 593-603, 1998.
15. Manara, G., A. Monorchio, and R. Reggiannini, "A space-time discretization criterion for a stable time-marching solution of the electric ¯eld integral equation," IEEE Trans. Antennas Propagat., Vol. 45, No. 3, 527-532, 1997.
16. Dwight, H. B., Tables of Integrals and Other Mathematical Data, 3rd Ed., The Macmillan Company, 1957.
17. Rao, S. M., Time Domain Electromagnetics, Academic Press, New York, 1999.
18. Geranmayeh, A., W. Ackermann, and T. Weiland, "Survey of temporal basis functions for integral equation method," Proc. 7th IEEE Workshop on Computational Electromagnetics in Time-Domain, CEM-TD' 07, Vol. 533, 1-4, Perugia, Italy, 2007.