In this paper, a theoretical analysis of numerical dispersion of the three-dimensional (3-D) high-order finite-difference time-domain (FDTD) method with weighted Laguerre polynomials (WLPs) is presented. The phase velocity of numerical wave modes is relevant to the direction of wave propagation, grid discretization and time-scale factor. The formula to determine a suitable time-scale factor is derived. By a theoretical evaluation, the dispersion errors for the 3-D high-order WLP-FDTD scheme with different time-scale factors are obtained. Finally, one numerical example is included to validate the effectiveness of the theoretical solution of the time-scale factor.
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