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In this paper, an accurate numerical dispersion relationship is developed for 3-D ADI FDTD with artificial anisotropy. The numerical dispersion relation with accurate mathematical model helps to calculate the anisotropic parameters, which are used to control the error of the numerical phase velocity. Numerical example shows that the proposed method helps to reduce the numerical dispersion significantly. The effects of anisotropic parameters on the numerical dispersion with different mesh resolution, courant number and cell dimension ratio, are shown for three-dimensional anisotropic ADI-FDTD. A comparison has been made for anisotropic ADI FTDD and conventional ADI FDTD in terms of accuracy and CPU time for the calculation of resonant frequencies of rectangular cavity.