时域有限差分法中的数值色散及误差分析

Numerical Dispersion and Error Analysis in Finite-Difference Time-Domain Method

本文给出了一种时域有限差分法(FDTD)的误差分析方法。通过分析波动过程中的色散方程,导出了数值色散关系的特征矩阵。利用量纲分析建立评价函数,详细讨论了在一维、二维及三维情形下的齐次波动方程FDTD求解时的数值有效性。结果表明数值波长是影响齐次波动方程数值收敛的最主要因素,验证了阻抗匹配媒质在FDTD计算中达到吸收电磁波的明显效果。

In this paper, a method of error analysis is proposed for the finite-difference time-domain(FDTD) method. Characteristic matrix of numerical dispersion is derived based on dispersion relation of the dispersion-equation in the wave motion. By using dimensional analysis, evaluation functions have been built up. Numerical availability for homogeneous wave equations is discussed in detail on the case of one-, two-, and three-dimensions. The numerical results are shown that the numerical-wavelength is the main factor to influence numerical convergence. In addition, impedance matched medium layer has been verified with absorbing electromagnetic wave obviously in the FDTD computation.