A high-order accurate scheme for solving the time-domain dispersive Maxwell's equations and material interfaces is described. Maxwell's equations are solved in second-order form for the electric field. A generalized dispersive material (GDM) model is used to represent a general class of linear dispersive materials and this model is implemented in the time-domain with the auxiliary differential equation (ADE) approach. The interior updates use our recently developed second-order and fourth-order accurate single-stage three-level space-time finite-difference schemes, and this paper extends these schemes to treat interfaces between different dispersive materials. Composite overlapping grids are used to treat complex geometry with Cartesian grids generally covering most of the domain and local conforming grids representing curved boundaries and interfaces. Compatibility conditions derived from the interface jump conditions and governing equations are used to derive accurate numerical interface conditions that define values at ghost points. Although some compatibility conditions couple the equations for the ghost points in tangential directions due to mixed-derivatives, it is shown how to decouple the equations to avoid solving a larger system of equations for all ghost points on the interface. The stability of the interface approximations is studied with mode analysis and it is shown that the schemes retain close to a CFL-one time-step restriction. Numerical results are presented in two and three space dimensions to confirm the accuracy and stability of the schemes. The schemes are verified using exact solutions for a planar interface, a disk in two-dimensions, and a solid sphere in three-dimensions.

描述了一种求解时域色散麦克斯韦方程和材料界面的高阶精确方案。麦克斯韦方程组以电场的二阶形式求解。广义色散材料（GDM）模型用于表示线性色散材料的一般类别，并且该模型在时域中使用辅助微分方程（ADE）方法实现。内部更新使用了我们最近开发的二阶和四阶精确单级三级时空有限差分方案，本文将这些方案扩展为处理不同分散材料之间的界面。复合重叠网格用于处理复杂的几何图形，而笛卡尔网格通常覆盖代表弯曲边界和界面的大部分域和局部符合网格。从界面跳变条件和控制方程式得出的兼容性条件可用于得出准确的数字界面条件，这些条件定义了幻影点处的值。尽管由于混合导数，某些兼容性条件在切线方向上耦合了重影点的方程，但仍显示了如何对方程进行解耦，以避免为接口上的所有重影点求解更大的方程组。通过模态分析研究了界面近似的稳定性，结果表明该方案保持了接近 从界面跳变条件和控制方程式得出的兼容性条件可用于得出精确的数字界面条件，这些条件定义了幻影点处的值。尽管由于混合导数，某些兼容性条件在切线方向上耦合了重影点的方程，但仍显示了如何对方程进行解耦，以避免为接口上的所有重影点求解更大的方程组。通过模态分析研究了界面近似的稳定性，结果表明该方案保持了接近 从界面跳变条件和控制方程式得出的兼容性条件可用于得出准确的数字界面条件，这些条件定义了幻影点处的值。尽管由于混合导数，某些兼容性条件在切线方向上耦合了重影点的方程，但仍显示了如何对方程进行解耦，以避免为接口上的所有重影点求解更大的方程组。通过模态分析研究了界面近似的稳定性，结果表明该方案保持了接近 展示了如何解耦方程，以避免针对界面上的所有幻影点求解更大的方程组。通过模态分析研究了界面近似的稳定性，结果表明该方案保持了接近 展示了如何解耦方程，以避免针对界面上的所有幻影点求解更大的方程组。通过模态分析研究了界面近似的稳定性，结果表明该方案保持了接近CFL一时间步长限制。在两个和三个空间维度上给出了数值结果，以确认该方案的准确性和稳定性。使用平面界面，二维圆盘和三维实心球的精确解验证了这些方案。