The Solution of Time-Domain Electric Field Integral Equations via Problem-Independent Inversion of the Laplace Transform

Abstract

This thesis derives and validates a new computational electromagnetic formulation via the re-initialized numerical inverse of the Laplace transform (NILTn) for solutions of two-dimensional and three-dimensional time-domain electrical-field integral equations (TD-EFIE) via the Method of Moments (MoM). The TD solution is found with a high degree of temporal accuracy and ensuring mathematical stability (L-stable), while taking relatively large time-steps. As a bonus, this formulation can accurately determine the frequency-domain (FD) solution of the EFIE via a fast-Fourier-transform of the interpolated TD solution. The interpolated TD solution is found using the information available via the NILTn to interpolate the non-interpolated TD waveform with minimal computational cost. The use of the re-initialized NILTn to solve the TD-EFIE was inspired by its application in TD lumped circuit analysis. The results are proven via various 2D and 3D examples and comparing both the TD and FD results to well-known computational electromagnetic methods.