CPML在3维HIE-FDTD算法中的实现

The complementation of CPML in 3-D HIE- FDTD algorithm

文中将CPML引入3维弱无条件稳定算法HIE-FDTD中,详细推到了CPML在3维弱无条件稳定HIE-FDTD中的差分公式。为了验证CPML在3维HIE-FDTD中的吸波性能,建立了数值计算模型,并将CPML的吸波性能同其它几种常用的吸收边界条件进行了比较。结果显示,当将CPML层数设置为8时,其最大反射误差为-72 d B,远低于传统FDTD方法的反射误差。另外,当匹配层参数设置为α=0.05,可以在一个较大范围内选取κmax和σmax来实现最佳误差,从而使得在选值时易于预测反射情况。

In this paper,an implementation of CFS-PML using auxiliary differential equation（ADE） for HIE-FDTD has been introduced in 3-D weakly conditionally stable HIE-FDTD,and its difference formula have been developed detailedly.In order to check its wave absorptivity,the computational model has been built and its wave absorptivity has been compared with other normal used wave absorptivity conditions.The results show that when evaluates 8 CPML layers,its maximal reflection error is-72 d B,and that higherly lower than that of FDTD. For the more,when we choose α=0.05 we can achieve maximal reflection error in a large area by choosing κmaxand σmax.And that is very useful to help us predict the complexion about reflection error.