快速时域有限差分方法计算矩形缺陷接地结构

摘要

It is time-consuming to calculate the transmission parameters of the rectangle defected ground structure (RDGS)using the conventional finite difference time domain method (FDTD) due to the Courant-Friedrich-Levy (CFL) limitation. The Crank-Nicolson FDTD(CN-FDTD),which is an unconditionally stable scheme, is adopted in this paper for improving the efficiency of the computation. The efficiency and the precision are analyzed in detail with the different time steps. The numerical results show that the CN-FDTD scheme is stable and efficient, even if the time step is far beyond the CFL limit. The results with the CN-FDTD show good agreement with the ones using the conventional FDTD,and the efficiency of the CN- FDTD scheme improves by 77.2%. In addition,the results using CN-FDTD is much more accurate than the ones with ADI-FDTD if the same time step is utilized.%Courant—Friedrich—Levy（CFL）稳定性条件会限制传统时域有限差分（FDTD）时间步长的选择，因此，采用传统FDTD对矩形缺陷接地结构（RDGS）传输系数（S21）进行计算，需要耗费大量的计算时间。为了节省计算时间，提高计算效率，采用无条件稳定的Crank—Nicolson格式FDTD（CN—FDTD）对RDGS传输系数进行计算，详细讨论了CN—FDTD时间步长与计算效率和计算精度的关系。数值结果表明：当CN—FDTD时间步长取值远大于CFL时间步长时，其计算结果与传统FDTD计算结果仍然吻合，同时计算效率能提高77．2％。比较了CN—FDTD和ADI—FDTD的计算误差，在时间步长取值相同的情况下，CN—FDTD的计算误差要远小于ADI—FDTD。