The plane-wave time-domain algorithm for the fast 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 matching-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 multilevel PWTD-enhanced MOT schemes, scales as O(N/sub t/N/sub s//sup 1.5/ log N/sub s/) and O(N/sub t/N/sub s/log/sup 2/N/sub s/), respectively, when the surface source density is represented by N/sub s/ spatial and N/sub 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(N/sub t/N/sub s//sup 2/). Therefore, PWTD-enhanced MOT schemes make possible the analysis of broadband scattering from structures of unprecedented dimensions.