We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately resolve fine structures that develop due to the varying material properties. Numerical examples demonstrate the effectiveness of the proposed method in handling temporal variation and its efficiency relative to traditional 2nd-order FDTD.

翻译：我们针对电磁特性在空间和时间上变化的材料，提出了一种适用于麦克斯韦方程组的有限体积方法。我们研究了守恒型与非守恒型两种数值格式。高阶方法能够精确解析因材料特性变化而产生的精细结构。数值算例表明，所提方法在处理时间变化方面具有有效性，且相较于传统的二阶时域有限差分法（FDTD）具有更高的效率。