Evaluation of the Green´s 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 Green´s function computed for many source-to-field distances ρ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green´s functions G_v(ρ,t) and G_A(ρ,t) for a multilayered medium for many ρ´s and t´s 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 ω so that the surface wave poles are lifted off the real k_ρ 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_ρ axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green´s function is calculated for many values of ρ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of ρG_v(ρ,t) versus ρ and t and demonstrate the space-time evolution of these Green´s 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 ρ) × 168 (points in t) uniformly spaced values of G_v(ρ,t) on an 867-MHz Pentium PC.