基于非条件稳定时域有限差分法的传输线瞬态分析

讨论了非条件稳定交替方向隐式(ADI)时域有限差分法(FDTD),把ADI-FDTD应用于传输线瞬态分析,首次推导出基于ADI-FDTD算法的传输线电报方程迭代公式,定义了传输线边界条件,进行了非条件稳定性的理论证明。该方法克服了Courant稳定条件的限制,时间步长只由数值色散误差来确定。计算结果表明,该方法与传统的FDTD的计算结果吻合,可以大大提高计算效率,对于长时间才能稳定的问题具有较高的使用价值。

Transient analysis of transmission lines based unconditionally stable FDTD method

An unconditionally stable Finite Difference Time Domain (FDTD) method using the principle of Alternating Direction Implicit (ADI) is presented. The ADI-FDTD is used to transient analysis of transmission line. The relation of telegraph equation recursion of the transmission line based on ADI-FDTD is derived. The terminal conditions of the transmission line are defined. The unconditional stability of the ADI-FDTD is theoretically analyzed. The ADI-FDTD overcomes the constraints of the Courant-Friedrich-Levy condition, and the maximum time step size is only limited by numerical errors. Results of numerical experiments confirm that the ADI-FDTD is consistent with the conventional FDTD; however, its efficiency is higher and it can be widely used in cases that long time is need to approach stable.