高阶ADI-FDTD算法的数值色散分析

该文给出高阶交替方向隐时域优先差分(ADI-FDTD)算法，即在ADI-FDTD迭代公式的基础上对时间的差分仍然采用二阶中心差分格式，而对空间的差分则采用四阶中心差分格式，并解析地证明了所给出的高阶ADI-FDTD算法仍然满足无条件稳定方程，同时对增长因子相位的分析，得到数值色散关系，最后对其数值色散误差进行了分析，研究表明与普通ADI-FDTD相比，其色散误差较小。

Analysis of the Numerical Dispersion of Higher Order ADI-FDTD

In this paper, a new higher order Alternating Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) formulation in particular, a second-order-in-time, fourth-order-in-space AD-FDTD method is presented for the first time. At the same time ,the unconditional stability of the higher order ADI-FDTD formulation is analytically proved. By analysis of the amplification factors, the numerical dispersion relation is derived. In addition, the numerical dispersion errors are investigated. Finally numerical results indicate that the higher order ADI-FDTD has s better accuracy compared to the ADI-FDTD method.