二维US-FDTD方法的数值稳定和色散分析

Analyzing Numerical Stability and Dispersion of 2-D US-FDTD

研究了二维US-FDTD方法的数值稳定性和数值色散特性。通过对增长因子的计算,证明了US-FDTD方法的无条件稳定性。利用增长因子的相位,推导出了US-FDTD方法的数值色散关系式。分析了US-FDTD方法的数值色散误差。数值分析表明,与ADI-FDTD方法一样,数值色散误差仍然是决定US-FDTD时间步长选取的关键因素。同时发现,数值色散受时间步长及网格大小的影响。

The numerical stability and dispersion properties of the two dimensional(2-D) US-FDTD method is studied.First,the unconditional numerical stability of the US-FDTD is proved through computing the amplification factor.Then,by analysis of the phase of the amplification factor,the numerical dispersion relation is derived.Finally,the numerical relation errors caused by the US-FDTD are investigated.Numerical analysis results indicate that the numerical dispersion errors are also the key factor determining the time step in the US-FDTD method as in the ADI-FDTD method.It is also find that the numerical dispersion is affected by the selected time step,the shape and mesh resolution of the unit.