In this communication, the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is extended to analyze periodic structures. In the implicit updates of the ADI-FDTD method, the periodic boundary condition leads to a cyclic matrix. Instead of inverting the cyclic matrix directly, the problem is converted into two auxiliary linear systems that can be solved using the tridiagonal matrix solver. Consequently, only 7n arithmetic operations are required for each implicit update and the efficiency of the ADI-FDTD method is retained. Numerical examples further demonstrate the effectiveness of this periodic ADI-FDTD method.
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Wang et al. (2005) studied this question.
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