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.

翻译：建立了一种高效的时域有限差分（FDTD）算法，用于求解含非均匀介质电介质材料中的横向电场二维麦克斯韦方程，其中电场在电介质界面处不连续。该新算法基于麦克斯韦方程的积分形式以及跨界面电场的关联关系推导而成。它是对轮廓路径有效介电常数算法的一种改进，通过在公式中引入额外项来实现。该方案在求解电介质圆柱散射问题时，通过与米氏理论精确解进行验证，并与上述轮廓路径法、常规阶梯法和体积平均法进行了比较。数值结果表明，新算法在精度上较其他方法有显著提升。此外，该算法结构简单，可非常容易地集成到任何现有的FDTD软件包中。