三维周期结构弱无条件稳定时域有限差分算法

Weakly conditionally stable 3-D FDTD method for periodic structures

从麦克斯韦方程出发,导出了适用于周期结构的三维弱无条件稳定时域有限差分(FDTD)算法的迭代式,在理论上证明了其稳定性条件,其稳定性条件比普通FDTD的稳定性条件要宽松,并将周期边界条件应用到迭代式中,得到了可直接编程迭代的方程,给出了对其特有的一类非三对角阵的解决办法。最后通过算例将计算结果与常规FDTD及ADI-FDTD计算结果比较,验证了算法的精确性和有效性。

Based on Maxwell＇ s equations, a weakly conditionally stable finite-difference time domain（FDTD） method for periodic structures is proposed. The stability condition is verified theoretically. Which is looser than that of the conventional FDTD method. And the ShermamMorrison formula has been used to solve the nomtridiagonal linear system. The new algorithm has better accuracy and efficiency than the ADLFDTD, especially for large time step size. A numerical example is presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the CPU time for this method can be reduced to about 33% of the ADI-FDTD method.