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 subsequently provide a detailed stability analysis with a generalization of the Courant criterion to the dynamic regime. 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.

翻译：我们提出了一种通用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(1+1)方案进行的局部自适应和二维扩展（2+1）。由于广义Yee元胞与传统Yee元胞固有的匹配特性，这种局部自适应将文献[1]方案的适用范围扩展到包含多速度分布和任意速度分布的复杂运动结构，同时完全兼容传统吸收边界条件及介质色散的标准处理方法。研究表明，直接应用传统FDTD方案能预测定性正确的光谱跃迁，但定量上会产生错误的散射振幅。基于此观测，我们推导出在实验室系中自动满足运动边界条件的广义混合物理场与辅助场（非物理场），并据此建立了基于相应麦克斯韦方程组与本构关系的局部更新方程。随后，将Courant准则推广至动态情形，给出了详细的稳定性分析。最终通过多个代表性算例验证和展示了所提方法。该方案填补了计算电磁学公开文献的重要空白，为商业软件平台中运动结构的求解提供了前所未有的直接解决方案。