无时间约束FDTD方法在三维散射中的应用

本文阐述了一种无时间约束条件的FDTD方法(ADI-FDTD)在三维目标电磁散射中的应用.由于散射问题的复杂性,文中分别推导了ADI-FDTD原始方程在连接边界条件、吸收边界条件和近远场外推等关键处的修正方程,并提出了ADI-FDTD方法中的时间步长上限.通过算例表明该方法与传统FDTD方法相比,时间步长可突破传统时间－空间约束条件,它的选取能远大于原有时间步长,对同一散射问题,总计算时间步可以相应大幅度减少,进而提高FDTD方法在计算散射问题中的效率.最后,数值计算显示了该方法的计算精度,并通过图表给出与传统FDTD计算时间的比较.

Three-Dimensional Scattering Analysis Using ADI-FDTD Method

This paper presents an alternating direction implicit FDTD (ADI-FDTD) algorithm without the Courant-Friedrich-Levy condition restraint for obtaining the solution of the three dimensional scattering problem.The perfectly matched layers are adopted to simulate the infinite space.The modified formulations of the connective boundaries are also given in detail.Compared with the conventional FDTD,the timestep increment is free from the CFL condition.So the total timestep is decreased significantly and the new algorithm is more efficient than traditional FDTD in terms of CPU time.Finally,some numerical results are given to demonstrate the accuracy and the high efficiency of ADI-FDTD.