The standard Yee FDTD algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of this classical scheme to 3D unstructured co-volume meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This circumvents the problem of accuracy losses, which are normally associated with the use of a staircased representation of curved material interfaces in the standard Yee scheme. The procedure has been successfully employed for modelling problems involving both isotropic and anisotropic lossy materials. Here, we consider the novel extension of this approach to allow for the challenging modelling of chiral materials, where the material parameters are frequency dependent. To adequately model the dispersive behaviour, the Z-transform is employed, using second order Pade approximations to maintain the accuracy of the basic scheme. To validate the implementation, the numerical results produced are compared with available analytical solutions. The stability of the chiral algorithm is also studied.

中文翻译：

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在非结构化网格上使用 3D 跳蛙方案对任意形状的色散手征介电物体进行 EM 建模

标准 Yee FDTD 算法因其简单性和无发散性而广泛用于计算电磁学。基于 Delaunay 原始网格及其高质量 Voronoi 对偶的使用，采用了这种经典方案对 3D 非结构化共体积网格的推广。这避免了精度损失的问题，这通常与在标准 Yee 方案中使用弯曲材料界面的阶梯表示相关。该过程已成功用于建模涉及各向同性和各向异性有损材料的问题。在这里，我们考虑了这种方法的新颖扩展，以允许具有挑战性的手性材料建模，其中材料参数与频率相关。为了充分模拟色散行为，采用 Z 变换，使用二阶 Pade 近似来保持基本方案的准确性。为了验证实施，将产生的数值结果与可用的解析解进行比较。还研究了手征算法的稳定性。