In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell’s equations with embedded perfect electric conductor boundary conditions. The CFM uses a minimization procedure to compute a correction to a given FD scheme in the vicinity of the embedded boundary to retain its order. The minimization problem associated with CFM approaches is analyzed in the context of Maxwell’s equations with embedded boundaries. In order to obtain a well-posed minimization problem, we propose fictitious interfaces to fulfill the lack of information, namely the surface current and charge density, on the embedded boundary. We introduce CFM-FDTD schemes based on the well-known Yee scheme and a fourth-order staggered FDTD scheme. We investigate the stability of these CFM-FDTD schemes using long time simulations. Convergence studies are performed in 2-D for various geometries of the embedded boundary. CFM-FDTD schemes have shown high-order convergence.

在这项工作中，我们提出了基于校正函数方法 (CFM) 的交错 FDTD 方案，以离散化具有嵌入完美电导体边界条件的麦克斯韦方程组。CFM 使用最小化程序来计算对嵌入边界附近的给定 FD 方案的修正，以保持其顺序。与 CFM 方法相关的最小化问题在具有嵌入边界的麦克斯韦方程组中进行了分析。为了获得适定的最小化问题，我们提出了虚拟接口来满足嵌入边界上的信息缺乏，即表面电流和电荷密度。我们介绍了基于著名的 Yee 方案和四阶交错 FDTD 方案的 CFM-FDTD 方案。我们使用长时间模拟来研究这些 CFM-FDTD 方案的稳定性。对于嵌入边界的各种几何形状，在 2-D 中执行收敛研究。CFM-FDTD 方案已显示出高阶收敛性。