An Efficient Method of Moments and Automatic Differentiation Technique for Fast Parametric Analysis of Antennas

Traditionally, the asymptotic waveform evaluation (AWE) technique is combined with the method of moments (MoM) to perform fast frequency sweep calculations. In this approach, the unknown current distribution within the frequency band of interest is expanded using a Taylor or Padè approximation around a single frequency. The derivatives of the impedance matrix and excitation vector are computed based on the formulation proposed by C. R. Cockrell, et al. [C. R. Cockrell, and F. B. Beck, “Asymptotic Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis,” NASA Tech. Memo., 110292, 1996]. Based on this initial work, several researchers have extended the technique to fast integral solver, such as the fast multipole method (FMM) [X. C. Wei, and Y. J. Zhang, “The Hybridization of Fast Multipole Method with Asymptotic Waveform Evaluation for the Fast Monostatic RCS Computation,” IEEE Trans. Antennas Propag., 52(2), 2004] and the adaptive integral method (AIM) [X. Wang, S. Gong, J. Guo, Y. Liu, and P. Zhang, “Fast and Accurate Wide-band Analysis of Antennas Mounted on Conducting Platform Using AIM and Asymptotic Waveform Evaluation Technique,” IEEE Trans. Antennas Propag., 59(12), 2011]. In all these approaches, the antenna impedance response over a band of frequencies is evaluated, eliminating the need for expensive matrix inversion. However, at the design stage, parametric analysis of antenna variables is performed to evaluate the antenna performance. This process requires a significant number of simulations, which are often computationally expensive.