In this letter, a theoretical analysis of the numerical dispersion and key parameter selection of the finite-difference time-domain (FDTD) method with weighted Laguerre polynomials is presented. Different from the conventional FDTD method, the numerical dispersion relation is relevant not only to sampling point density in space domain but also to time-scale factor. For a fixed relative error of phase velocity, the suitable sampling point density and time-scale factor can be determined. In addition, the selection of the number of Laguerre functions is derived using the theoretical time-scale factor, and is verified in a numerical example.
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Chen et al. (2013) studied this question.