无条件稳定时域有限差分法综述

A Summary of Unconditionally Stable Finite Difference Time Domain Methods

时域有限差分法(FDTD)是解决复杂电磁问题的有效方法之一,可以对电磁问题进行直观的描述,且容易编程分析,已经发展成为一种成熟的数值计算方法。然而,传统FDTD算法的时间步长收到了稳定性条件的限制,这使得FDTD方法的计算效率和应用范围受到了限制,因此无条件稳定算法应运而生,人们提出了多种形式的无条件稳定FDTD算法。本文介绍并分析了几种无条件稳定的时域有限差分法,给出了具有一定参考价值的结论。

Finite Difference Time Domain（FDTD） is one of the effective methods to solve complex electromagnetic problems. It can describe electromagnetic problems intuitively and is easy to program and analyze. It has developed into a mature numerical calculation method. However, the time step of the traditional FDTD algorithm is limited by the stability conditions, which limits the computational efficiency and application range of the FDTD method. Therefore, the unconditional stability algorithm emerges at the historic moment and many forms of unconditional stable FDTD algorithm have been proposed. This paper introduces and analyzes several unconditionally stable FDTD methods, and gives some conclusions with certain reference value.