We present a generalized FDTD scheme to simulate moving electromagnetic structures with arbitrary space-time configurations. This scheme is a local adaptation and 2+1-dimensional extension of the uniform and 1+1-dimensional scheme recently reported in [1]. 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 [1] to moving structures that involve multiple and arbitrary velocity profiles while being fully compatible with 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 (non-physical) - 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 relations. We finally validate and illustrate the proposed method by three canonical examples - a space-time interface, a space-time wedge and a space-time accelerated interface - whose combination represent arbitrary space-time configurations. 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.

翻译：我们提出了一种广义FDTD方案，用于模拟具有任意时空构型的运动电磁结构。该方案是对近期文献[1]中报道的均匀一维+一维方案进行局部适配和二维+一维扩展的结果。由于广义Yee单元与传统Yee单元固有的匹配特性，局部适配使得[1]中方案的适用范围得以扩展至包含多重且任意速度分布的运动结构，同时能够完全兼容常规吸收边界条件和介质色散的标准处理方法。研究表明，直接应用传统FDTD方案虽能预测定性正确的光谱跃迁，但会产生定量错误的散射振幅；基于这一发现，我们推断出在实验室坐标系中自动满足运动边界条件的广义混合场（物理场与辅助非物理场），并据此建立基于相关麦克斯韦方程组及本构关系的局部更新方程。最后，通过三个典型实例（时空界面、时空楔形体及时空加速界面）对提出的方法进行了验证与阐释，这些实例的组合可表征任意时空构型。该方案填补了计算电磁学公开文献中的重要空白，为商业软件平台中的运动结构提供了前所未有的直接求解方案。