适用于ADI-FDTD的基于线性插值的吸收边界条件及其改进方法

摘要

基于线性插值的方法提出了一种适用于交替方向隐式时域有限差分法(ADI-FDTD)的吸收边界条件,该边界条件能够在ADI-FDTD方法中改善边界反射性能.首先,对由截断误差和相速估计误差引起的此吸收边界条件的反射进行了分析和推导.通过理论分析,说明了基于相速估计和非均匀网格的对此吸收边界改进方法能够改善边界条件的反射特性.然后进行了矩形波导情况下该吸收边界条件的数值仿真.最后给出了数值仿真结果,并通过对有无相速估计下吸收边界条件反射系数比较、对均匀和非均匀网格处理下吸收边界条件反射系数的比较,以及对在不同时间步长下吸收边界条件反射系数变化的分析,说明了该吸收边界条件及其改进方法对ADI-FDTD方法中的边界反射性能有很好的改善效果.%With the linear interpolation method, an improved absorbing boundary condition(ABC) is introduced and derived, which is suitable for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method.The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed.Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC.A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation.According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing.The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on theabsorption.Numerical results obviously show that efficientimprovement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.