Closed form evaluation of time domain fields due to Rao-Wilton-Glisson sources for use in marching-on-in-time based EFIE solvers

Often, spatial Rao-Wilton-Glisson (RWG) functions with polynomial temporal signatures are used in the construction of marching-on-in-time (MOT) based electric field integral equation (EFIE) solvers. While the efficient evaluation of fields generated by RWG sources with time-harmonic temporal dependence has been studied extensively, the same is not true for transient RWG sources. Here, it is shown that the convolution between RWG sources with polynomial signatures and the three-dimensional time domain free space Green's function can be evaluated exactly.