Empirical Comparison of Envelope-Tracking and Time-Domain Adaptive Integral Methods for Surface Integral Equations

TL;DR

This paper compares the efficiency and accuracy of envelope-tracking and time-domain adaptive integral methods for electromagnetic scattering, demonstrating ET-AIM's advantages in narrowband and complex scenarios.

Contribution

It provides a comprehensive evaluation of ET-AIM against TD-AIM, optimizing key parameters and highlighting ET-AIM's superior performance in certain regimes.

Findings

ET-AIM and TD-AIM have similar times for wide bandwidths.

ET-AIM's costs decrease significantly for bandwidths under 50%.

ET-AIM efficiently handles large, complex scattering problems.

Abstract

This paper presents a detailed evaluation of the envelope-tracking adaptive integral method (ET-AIM), an FFT-accelerated algorithm for analyzing electromagnetic scattering. ET-AIM is used to solve progressively more complex benchmark scattering problems and key parameters of the method (the auxiliary grid size, near-zone size, temporal basis function type, time-step size, and iterative solver tolerance) are optimized. The computational costs and accuracy of ET-AIM are compared to its time-domain counterpart, the time-domain adaptive integral method (TD-AIM), in the high-frequency regime, where the spatial discretization of the scattering object is determined by the minimum wavelength of interest rather than its geometrical features. Numerical results show that although ET-AIM and TD-AIM computation times are comparable when the bandwidth of interest is wide, the ET-AIM marching costs are dominated by iterative solution rather than scattered-field computations ('right-hand-side' computations) and that as the bandwidth of interest becomes narrower than 50% of the center frequency, ET-AIM computational costs become significantly smaller than TD-AIM ones. ET-AIM is also shown to efficiently solve large and complex scattering problems whose solution by TD-AIM is impractical.