The plane-wave time-domain algorithm for the fast analysis oftransient wave phenomena

摘要

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(NtNs1.5 log Ns) and O(N tNslog2Ns), respectively, when the surface source density is represented by Ns spatial and Nt 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