二维TE波中的HIE-CPML算法

文中将坐标伸缩完全匹配层CPML引入到弱无条件稳定算法HIE-FDTD中研究其吸波性能。详细推导了2维TE波模型中CPML在HIE-FDTD算法中应用的差分公式。为检验本文所提方法的吸波效能，建立了计算模型，将其与其它吸收边界条件的吸波性能进行了综合比较，计算了HIE-FDTD算法选取不同条件数时的反射误差，并详细说明如何合理选取α，κmax和σmax来实现最佳相对误差。结果显示：当将本文所提方法的CPML层数设置为8时，其反射误差为-62 dB，低于传统FDTD方法的-58 dB；当选取α=0.05，κmax=10，σmax/σopt=1.3可以实现低至-83 dB的最大相对误差；在仿真中，其比传统FDTD方法也约减少48%的计算时间。

HIE-CPML algorithm in the 2D TE wave model

In this paper, An implementation of CFS-PML using auxiliary differential equation （ADE） for HIE-FDTD is developed. their idiographic difference formula in the TE wave model have been proposed. And 1n order to check its wave absorptivity, the computational model has been built and its wave absorptivity has been compared with other methods, the reflection error which caused by different CFL numbers has been computed, and explains how to choose α, κmax and σmax to achieve optimal reflection error rationally. the numeraical results show that when CPML number is 8, its reflection error is-62 dB that lower than FDTD method’s-58 dB, and when choosingα=0.05,κmax=10 andσmax/σopt=1.3 its maximal reflection error can be as low as-83 dB, in the simulation, its computation time decreases 48%than that of FDTD methods.