In a time domain Marching-on-in-degree (MOD) solver based on a Galerkin implementation of the Method of Moments (MoM), it is observed that the matrix elements for the matrix to be inverted contain integrals that are similar to the ones encountered in a frequency domain MoM solver using the piecewise triangular patch basis functions. It is also observed that the error in the evaluation of the matrix elements involving these integrals are larger in the time domain than those involved in the frequency domain MoM solvers. The objective of this paper is to explain this dichotomy and how to improve upon them when using the triangular patch basis functions for both the time and the frequency domain techniques. When the distance between the two triangular patches involved in the evaluation of the matrix elements, are close to each other or when the degree of the Laguerre polynomial in a MOD method is high, the integral accuracy will be compromised and the number of sampling points to evaluate the integrals need to be increased. Numerical results are presented to illustrate this point.
2. 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
3. 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
4. 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
5. Chung, Y. S., T. K. Sarkar, B. H. Jung, M. Salazar-Palma, Z. Ji, S. Jang, and K. Kim, "Solution of time domain electric field integral equation using Laguerre polynomials," IEEE Trans. Antennas and Propagat., Vol. 52, No. 9, 2319-2323, Sept. 2004.
doi:10.1109/TAP.2004.835248
6. Jung, B. H., T. K. Sarkar, Y. S. Chung, M. Salazar-Palma, Z. Ji, S. Jang, and K. Kim, "Transient electromagnetic scattering from dielectric objects using electric field integral equation with Laguerre polynomials as temporal basis functions," IEEE Trans. Antennas and Propagat., Vol. 52, No. 9, 2329-2340, Sept. 2004.
doi:10.1109/TAP.2004.834062
7. Ji, Z., T. K. Sarkar, B. H. Jung, Y. S. Chung, M. Salazar-Palma, and M. Yuan, "A stable solution of time domain electric field integral equation for thin-wire antenna using the Laguerre polynomials," IEEE Trans. Antennas and Propagat., Vol. 52, No. 10, 2641-2649, Oct. 2004.
8. Ji, Z., T. K. Sarkar, B. H. Jung, M. Yuan, and M. Salazar-Palma, "Solving time domain electric field integral equation without the time variable," IEEE Trans. Antennas and Propagat., Vol. 54, No. 1, 258-262, Jan. 2006.
doi:10.1109/TAP.2005.861515
9. Jung, B. H., et al., Time and Frequency Domain Solutions of EM Problems Using Integral Equations and a Hybrid Methodology, John Wiley & Sons, Inc., 2010.
doi:10.1002/9780470892329
10. Mei, Z., Y. Zhang, T. K. Sarkar, B. H. Jung, A. Garcia-Lamperez, and M. Salazar-Palma, "An improved marching-on-in-degree method using a new temporal basis," IEEE Trans. Antennas and Propagat., Vol. 59, No. 12, 4643-4650, Dec. 2011.
doi:10.1109/TAP.2011.2165482
11. Mei, Z., Y. Zhang, T. K. Sarkar, M. Salazar-Palma, and B. H. Jung, "Analysis of arbitrary frequency-dependent losses associated with conducting structures in a time-domain electric field integral equation," IEEE Antennas Wireless Propag. Lett., Vol. 10, 678-681, 2011.
12. Rao, S. M., "Electromagnetic scattering and radiation of arbitrarily-shaped surfaces by triangular patch modeling,", Ph.D. Dissertation, Univ. Mississippi, Aug. 1980.
13. Rao, S. M., D. R. Wilton, A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagat., Vol. 30, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818
14. Poularikas, A. D., The Transforms and Applications Handbook, 2nd Ed., CRC Press, 2000.
doi:10.1201/9781420036756
15. Gradshteyn, I. S. and I. M. Ryzhik, "Table of Integrals, Series, and Products," Academic Press, New York, 1999.
16. Dunavant, D. A., "High degree efficient symmetrical Gaussian quadrature rules for the triangle," Int. J. Num. Meth. Eng., Vol. 21, 1129-1148, 1985.
doi:10.1002/nme.1620210612
Submit
