The plane-wave time-domain algorithm for the past analysis of transient wave phenomena

This article describes a plane-wave time-domain (PWTD) algorithm that facilitates the fast evaluation of transient wave fields produced by surface scattering. The algorithm presented relies on a Whittaker-type expansion of transient fields in terms of propagating plane waves. The incorporation of the PWTD scheme into existing marching-on-in-time- (MOT-) based integral-equation solvers is elucidated. It is shown that the computational cost of performing a surface-scattering analysis, using two-level and multi-level PWTD-enhanced MOT schemes, scales as O(NtNs1.5 logN(s)) and O(NtNs log(2) N-s),respectively, when the surface source density is represented by N-s spatial and N-t temporal samples. Hence, the computational cost of the proposed algorithms scales much more favorably than that of classical MOT schemes, which scale as O(NtNs2). Therefore, PWTD-enhanced MOT schemes make possible the analysis of broadband scattering from structures of unprecedented dimensions.