Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm

A fast algorithm is presented for solving electric, magnetic, and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near-fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as O(N_iN_s^2/3 log N_s) as opposed to 𝒪(N_tN_s²) for classical MOT methods, where N_t and N_s are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented