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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 method (FDTD) based on split-step scheme and Crank-Nicolson scheme is proposed. The unconditional stability of this algorithm is also proved. The proposed algorithm uses a new form of matrix factorization to decompose three-dimensional problems into one-dimensional problems along the x, y and z directions. The proposed algorithm uses the alternating direction implicit (ADI) -FDTD algorithm and the split-step (SS) Compared with the SS-FDTD (2,2) algorithm, the FDTD (1,2) algorithm reduces the computational complexity and improves the computational efficiency. Meanwhile, the proposed algorithm has the second-order time accuracy and the second-order spatial accuracy. The new algorithm’s derivation procedure is simpler than the unconditional FDTD algorithm based on exponential factorization. Compared with the ADI-FDTD algorithm, the new algorithm can be used to calculate the resonant cavity structure. Compared with the SS-FDTD (1,2) algorithm, the proposed algorithm can save about 13.5% of the computational time.