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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 39 > pp. 1-45
## Time-Domain EFIE, MFIE, and CFIE Formulations Using Laguerre Polynomials as Temporal Basis Functions for the Analysis of Transient Scattering from Arbitrary Shaped Conducting StructuresBy B. H. Jung, Y.-S. Chung, and T. K. Sarkar
Abstract:
In this paper, we present time-domain integral equation (TDIE) formulations for analyzing transient electromagnetic responses from three-dimensional (3-D) arbitrary shaped closed conducting bodies using the time-domain electric field integral equation (TDEFIE), the time-domain magnetic field integral equation (TD-MFIE), and the time-domain combined field integral equation (TD-CFIE). Instead of the conventional marching-on in time (MOT) technique, the solution methods in this paper are based on the Galerkin's method that involves separate spatial and temporal testing procedure. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D structures. The timedomain unknown coefficient is approximated by using an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as temporal testing. Using these Laguerre functions it is possible to evaluate the time derivatives in an analytic fashion. We also propose a second alternative formulation to solve the TDIE. The methods to be described result in very accurate and stable transient responses from conducting objects. Detailed mathematical steps are included and representative numerical results are presented and compared.
2. Jung, B. H. and T. K. Sarkar, "Time-domain CFIE for the analysis of transient scattering from arbitrarily shaped 3D conducting objects," 3. Rao, S. M., 4. Rao, S. M. and D. R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape," 5. Vechinski, D. A. and S. M. Rao, "A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape," 6. Rao, S. M. and T. K. Sarkar, "An alternative version of the time-domain electric field integral equation for arbitrarily shaped conductors," 7. Rao, S. M. and T. K. Sarkar, "An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies," 8. Sarkar, T. K., W. Lee, and S. M. Rao, "Analysis of transient scattering from composite arbitrarily shaped complex structures," 9. Jung, B. H. and T. K. Sarkar, "Time-domain electric-field integral equation with central finite difference," 10. Jung, B. H. and T. K. Sarkar, "An accurate and stable implicit solution for transient scattering and radiation from wire structures," 11. Jung, B. H. and T. K. Sarkar, "Transient scattering from threedimensional conducting bodies by using magnetic field integral equation," 12. Sarkar, T. K. and J. Koh, "Generation of a wide-band electromagnetic response through a Laguerre expansion using early-time and low-frequency data," 13. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," 14. Wilton, D. R., S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," 15. Rao, S. M., "Electromagnetic scattering and radiation of arbitrarily- shaped surfaces by triangular patch modeling," 16. Van Bladel, J., 17. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three dimensional scattering problems," 18. Poularikas, A. D., 19. Gradshteyn, I. S. and I. M. Ryzhik, 20. Chung, Y. S., T. K. Sarkar, B. H. Jung, and J. Zhong, "Solution of time domain electric field integral equation using an unconditionally stable methodology," 21. Chung, Y. S, T. K. Sarkar, and B. H. Jung, "Solution of time domain magnetic field integral equation for arbitrarily closed conducting bodies using an unconditionally stable methodology," 22. Chung, Y. S., T. K. Sarkar, and B. H. Jung, "An unconditionslly stable scheme for finite difference time domain (FDTD) method," |

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