A generalized TDIE framework for arbitrary time basis functions

A generalized formulation of the TD-EFIE (time-domain electric field integral equation) is presented, extending the work of Y.S. Chung et al. (see IEEE Trans. Antennas Propag., vol.52, no.9, p.2319-28, 2004). The framework shows that, for a large class of basis functions, the time integration can be analytically removed from the calculation. This allows the time-space integral to be computed to arbitrary accuracy through existing quadrature schemes. The result is a single, large matrix problem that is adaptable to different solvers, including marching on in time, marching on in order, fast solvers, and parallel solvers. While the formulation presented is specifically for the EFIE, it is equally applicable to other TDIEs.