Fast Time Domain Integral Equation Solvers for Analyzing Two-Dimensional Scattering Phenomena; Part II: Full PWTD Acceleration

摘要

The primary impediment to using marching-on-in-time (MOT) schemes for solving time domain integral equations pertinent to the analysis of large-scale two-dimensional (2D) transient electromagnetic scattering phenomena is their high computational complexity. If N_s and N_t are the number of spatial and temporal degrees of freedom in the analysis, then this computational complexity scales as O (N_s~2 N_t~2. Recently, it has been theoretically demonstrated that if classical MOT schemes are augmented with 2D plane wave time domain (PWTD) algorithms, their computational complexity can be reduced to O(N_sN_t log N_t). This article elucidates key steps in implementing such a scheme within the context of 2D transient TM_z and TE_z electromagnetic scattering analysis. Several numerical examples that demonstrate the efficacy of the proposed schemes and also confirm the aforementioned computational complexity are presented.