三维最优时域有限差分方法

3-D Optimal Finite Difference Time Domain Method

数值色散是时域有限差分方法(FDTD)中最主要的误差来源,导致数值相速成为频率和方向的函数。文中讨论了一种基于最优有限冲激滤波器设计方法的最优差分格式,从频率空间或者波数空间中实现对理想偏微分算子的逼近,构造一种新的具有低数值色散关系的最优时域有限差分方法。文中导出了其数值色散关系和进行了稳定性分析,并通过与常用的基于泰勒级数展开定理的高阶(2,4)时域有限差分法相比较,发现最优时域有限差分法的数值色散得到了极大的改善。最后通过一个数值例子来验证其有效性。

A major source of error in the finite difference time domain （FDTD） method is the numerical dispersion, which makes the phase velocity variable with frequency and propagation direction. In this paper, a optimal finite difference scheme based on the optimal FIR method is discussed, with which the ideal differential operator is approximated in the frequency or spetial domain. Then, a low-dispersion optimal finite difference time domain method is presented. Through the analysis of the numerical dispersion and the stability, it can be found that its performance is superior to that of the conventional FDTD method. Finally, a simple numerical example is presented for its validity.