Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm

The computational complexity of classical marching-on-in-time (MOT) methods for solving time domain integral equations (TDIEs) pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as O(N_tN_s²) (N_t and N_s denote the number of temporal and spatial degrees of freedom (DOF) of the electric current on the target). This scaling law impedes the application of these schemes to the analysis of large-scale scattering phenomena. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based TDIE solvers. Previously, we described a two-level PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting targets; the computational complexity of this algorithm scales as O(N_tN_s^1.5logN_s). Here, a multilevel PWTD scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described. In addition, a multilevel PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting scatterers using O(N_tN_slog²N_s) CPU resources is outlined. Last, the accuracy and CPU/memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies.