Weakly conditionally stable 3-D FDTD method for periodic structures
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摘要: 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。Abstract: Based on Maxwells 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 Sherman-Morrison formula has been used to solve the non-tridiagonal linear system. The new algorithm has better accuracy and efficiency than the ADI-FDTD, 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.
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