新型无条件稳定SSCN-FDTD算法

A New Unconditionally-Stable SSCN-FDTD Method

提出了一种新型的基于split-step方案和Crank-Nicolson方案的时域有限差分法(finite-difference time-domain method FDTD),并且证明了此种算法的无条件稳定性。所提出的算法采用新的矩阵分解形式,沿着x、y、z三个方向进行分解,将三维问题转化为一维问题,与alternating direction implicit(ADI)-FDTD算法、split-step(SS)-FDTD(1,2)算法和SS-FDTD(2,2)算法相比,减少了计算复杂度,提高了计算效率;同时所提出的算法具有二阶时间精度和二阶空间精度。新型算法的推导程序比基于指数因子分解的无条件FDTD算法更简单。将新型算法用于计算谐振腔结构,在计算相对误差一致的情况下,计算时间比ADI-FDTD算法节省约31%,比SS-FDTD(1,2)算法节省约13.5%。

A new finite-difference time-domain （FDTD） method based on the split-step scheme and the Crank-Nicolson scheme is presented, which is proven to be unconditionally-stable. The proposed method has the new splitting＇forms of the matrix along the x, y and z coordinate directions, and it translates a 3-D problem into some I-D problems. Compared with the alternating direction implicit （ADI）-FDTD method, the split-step （SS）-FDTD （1, 2） method and the SS-FDTD （2, 2） method, the proposed method reduces computational complexity and enhances computational efficiency. Moreover, the proposed method has the second-order accuracy both in time and space, and has simpler procedure formulation than .the operator splitting （OS）-FDTD method based on the exponential evolution operator scheme. Furthermore, in the computation of the resonant frequencies of a cavity, in the condition of same relative errors, the saving in CPU time with the proposed method can be more than 31% in comparisons with the ADI-FDTD method and more than 13.5% in comparisons with the SS-FDTD（1,2） method.