On Analytical Evaluation of Retarded-Time Potentials for SWG Bases

The Radon transform interpretation of impulsively excited time-domain integrals is recently shown to provide the time samples of these integrals in closed analytical form. Here, the derivation of such formulas for the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Schaubert-Wilton-Glisson (SWG) basis function is accomplished. It was proven conceptually before that the aforementioned potentials are related to the geometrical quantities of the surface of intersection between the tetrahedral supports of the SWG basis and the hyper-cone centered at the observation point with radius ct where c is the speed of light. Analytical evaluation of these quantities involves proper introduction of the corresponding solid-angle and its gradient. Rigorously obtained formulas and numerical results are presented for them.