TDIE solver based on novel closed-form time-domain Green´s functions for half-space problem

New closed-form expressions for time-domain Green´s functions (TDGFs) for sources and observers residing in the interface of a half-space medium are presented. The proposed closed-form TDGF´s characterize scalar and vector potentials due to infinitesimal horizontal electric dipoles with Dirac delta temporal signature. The closed-form TDGFs are numerically validated by comparison with data derived using the Cagniard-de Hoop method. They also are used in a high-order accurate, marching-on-in-time-based time-domain integral equation (TDIE) solver. This TDIE solver calls for the computation of convolutions of TDGFs with temporal basis functions. Here, these convolutions too are cast in closed-form, assuming that the temporal basis function is a quadratic B-Spline (QBS). Numerical examples that demonstrate the applicability of the proposed scheme to the problem of scattering from planar PEC structures residing in the interface of a half-space medium are presented.