Exact evaluation of retarded-time potential integrals for the RWG bases

A new analytical approach for obtaining the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Rao-Wilton-Glisson (RWG) 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 RWG bases. To the best knowledge of the authors, analytical evaluation of the potential integrals due to the RWG bases have not been formulated prior to the present work either in the time domain or the frequency domain. It is shown that the aforementioned potentials are related to the arc segments formed by the intersection of the triangular supports of the RWG basis and the sphere 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 arc length and the vector potential is a function of the bisectors of these arc segments. A simple algorithm to evaluate these quantities is also presented. The validity of the obtained time-domain formulae is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain