色散媒质中ADI-FDTD

基于交替方向隐式(ADI)技术的时域有限差分(FDTD)法是一种非条件稳定的计算方法，该方法的时间步长不受Courant稳定条件限制，而由数值色散误差决定。与传统的FDTD相比，ADI-FDTD增大了时间步长，从而缩短了总的计算时间。本文采用递归卷积方法将ADI-FDTD推广应用于色散媒质，推导了二维情况下色散媒质中的ADI-FDTD迭代公式。应用推导公式计算了色散土壤中目标的散射，并与色散媒质FDTD结果对比，在大量减少计算时间的情况下，两者结果符合很好。

Unconditionally Stable ADI-FDTD for Dispersive Media

An implicit finite difference time domain method using the principle of the alternating direction implicit technique is unconditionally stable, and the maximum time step size is not limited by the Courant Friedrich Levy condition, but rather by numerical dispersion errors. Compared with the conventional FDTD method, the time step size of ADI FDTD can be enlarged arbitrarily. Therefore it takes less time to simulate. This paper extends ADI-FDTD to dispersive media based on recursive convolution(RC) method. Two-dimensional formulations for dispersive media are derived. Considering the scattering of two dimensional object buried in dispersive soil, as an example, the result of ADI FDTD for dispersive media agrees with the result of conventional FDTD and CPU cost is reduced obviously.