An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface. The new algorithm is derived based upon the integral version of the Maxwell's equations as well as the relationship between the electric fields across the interface. It is an improvement over the contour-path effective-permittivity algorithm by including some extra terms in the formulas. The scheme is validated in solving the scattering of a dielectric cylinder with exact solution from Mie theory and is then compared with the above contour-path method, the usual staircase and the volume-average method. The numerical results demonstrate that the new algorithm has achieved significant improvement in accuracy over the other methods. Furthermore, the algorithm has a simple structure and can be merged into any existing FDTD software package very easily.

中文翻译：

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二维麦克斯韦方程组的增强有限差分时域方法

构建了一种有效的时域有限差分 (FDTD) 算法，用于求解具有非均匀介电介质的横向电场 2D 麦克斯韦方程组，其中电场在介电界面上是不连续的。新算法是基于麦克斯韦方程组的积分形式以及界面电场之间的关系推导出来的。通过在公式中包含一些额外项，它是对轮廓路径有效介电常数算法的改进。该方案在用米氏理论的精确解求解介电圆柱体散射时得到验证，然后与上述等高线法、常用阶梯法和体积平均法进行比较。数值结果表明，与其他方法相比，新算法在精度上取得了显着的提高。此外，该算法结构简单，可以很容易地合并到任何现有的FDTD软件包中。