Evaluation of the Greens function for the mixed potential integral equation (MPIE) method in the time domain for layered media

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Greenʹs function computed for many source-to-field distances (rho) and time instants t. In this paper, a numerical method is used that computes the mixed potential Greenʹs functions G/sub v/((rho),t) and G/sub A/((rho),t) for a multilayered medium for many (rho)ʹs and tʹs simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex (omega) so that the surface wave poles are lifted off the real k/sub (rho)/ axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub (rho)/ axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Greenʹs function is calculated for many values of (rho) simultaneously. For a four-layer medium, we illustrate the numerical results by a threedimensional plot of (rho)G/sub v/((rho),t) versus (rho) and t and demonstrate the space-time evolution of these Greenʹs functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in (rho)) * 168 (points in t) uniformly spaced values of G/sub v/((rho),t) on an 867-MHz Pentium PC.