A Generalized FDTD Scheme for Moving Electromagnetic Structures With Arbitrary Space–Time Configurations
Amir Bahrami, Zoé-Lise Deck-Léger, Zhiyu Li, Christophe Caloz
Abstract
We present a generalized finite-difference time-domain (FDTD) scheme to simulate moving electromagnetic structures with arbitrary space–time configurations. This scheme is a local adaptation and 2+1-D extension of the uniform and 1+1-D scheme recently reported in Deck-Léger et al., 2023. The local adaptation, which is allowed by the inherently matched nature of the generalized Yee cell to the conventional Yee cell, extends the range of applicability of the scheme in Deck-Léger et al., 2023 to moving structures that involve multiple and arbitrary velocity profiles while being fully compatible with the conventional absorbing boundary conditions and standard treatments of medium dispersion. We show that a direct application of the conventional FDTD scheme predicts qualitatively correct spectral transitions but quantitatively erroneous scattering amplitudes, we infer from this observation generalized, hybrid—physical and auxiliary (nonphysical)—fields that automatically satisfy moving boundary conditions in the laboratory frame, and accordingly establish local update equations based on the related Maxwell’s equations and constitutive relationships. We subsequently provide a detailed stability analysis with a generalization of the Courant criterion for the generalized scheme. We finally validate and illustrate the proposed method by several representative examples. The proposed scheme fills an important gap in the open literature on computational electromagnetics and offers an unprecedented, direct solution for moving structures in commercial software platforms.