Fast Analysis of Transient Electromagnetic Scattering Using the Taylor Series Expansion-Enhanced Time-Domain Integral Equation Solver

This paper concentrates on an efficient fast algorithm for accelerating the marching-on-in-time-based time-domain integral equation method for the analysis of the transient electromagnetic scattering from perfect electrically conducting bodies. Taking advantage of the approximate evaluation of the vector and scalar potential terms and the Taylor series expansion of far field, the computational complexity and memory requirement of the proposed algorithm scale as
${\mathrm{ O}}(N_{t} N_{s} \log N_{s} )$
and
${\mathrm{ O}}(N_{s}^{1.5} )$
, respectively, where
$N_{t} $
and
$N_{s}$
denote the number of simulation time steps and spatial basis functions, respectively. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm.