三维周期结构弱无条件稳定FDTD算法研究

Implementation of UPML for weakly conditionally stable FDTD in periodic structures

将单轴完全匹配层UPML引入于弱无条件稳定算法LOD-FDTD中用于解决周期结构的电磁散射问题。在求解过程中,引入Sherman-Morrison方程解决迭代过程中产生的非三对角矩阵,显著提高了计算效率。为了检验本文所提方法的吸波效能,将其用于计算将带有细缝的周期阵列的反射系数,结果显示:当将本文所提方法的UPML层数设置为16时,其反射误差同传统FDTD方法的反射误差相当,当将本文所提方法的UPML层设置为4时,其反射误差比传统FDTD要低50dB。

In this paper, uniaxial perfectly matched layer （UPML） is applied in weakly conditionally stable FDTD method for periodic structures. In order to solve the special non-tridiagonal matrix, the Sherman-Morrison formula is applied, so the computational efficiency is improved. The reflection error of the proposed UPML absorber can be almost the same as the UPML absorber in the conventional FDTD method when the UPML is 16-layer. Even when the UPML is 4-layer, the reflection error can below -50 dB. Numerical results of reflection coefficient for the periodic array of metallic patches are calculated, so as to verify the accuracy and efficiency of the proposed method.