On the Evaluation of Retarded-Time Potentials for SWG Bases

A new approach for obtaining the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Schaubert-Wilton-Glisson (SWG) basis function is presented. The approach is formulated directly in the time domain without any assumptions regarding the temporal behavior of the currents represented by the SWG bases. It is shown that the aforementioned potentials are related to the solid angle formed by the intersection of the tetrahedral supports of the SWG basis and the "hyper-cone" that is centered at the observation point and that has a radius R = ct, where c is the speed of light. In particular, the scalar potential is directly proportional to the total solid angle, and the vector potential is a function of the area centroid vector of this solid angle. The validity of the obtained time-domain formulas is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain.