WCS-FDTD Algorithm for Periodic Structures

In this letter, the weakly conditional technique is applied to the finite-difference time-domain (FDTD) method, called WCS-FDTD in short. It is combined with periodic boundary condition (PBC), so periodic structures can be solved by using this method conveniently. When the explicit difference calculations are performed in the directions with larger spatial increments, the time-step is thus determined by the larger spatial increments, and the stability condition is less strict than the conventional FDTD method. In order to save the CPU running time, the Sherman-Morrison formula is used to solve the nontridiagonal linear systems. Compared to ADI-FDTD method, this method has better accuracy and computational efficiency. Numerical results are given to demonstrate the effectiveness of the proposed method.