REDUCTION OF NUMERICAL DISPERSION OF THE SIX-STAGES SPLIT-STEP UNCONDITIONALLY-STABLE FDTD METHOD WITH CONTROLLING PARAMETERS

A new approach to reduce the numerical dispersion of the six-stages split-step unconditionally-stable finite-difference time-domain (FDTD) method is presented, which is based on the split-step scheme and Crank-Nicolson scheme. Firstly, based on the matrix elements related to spatial derivatives along the x, y, and z coordinate directions, the matrix derived from the classical Maxwellʹs equations is split into six sub-matrices. Simultaneously, three controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into six sub-steps. Secondly, the analysis shows that the proposed method is unconditionally stable. Moreover, the dispersion relation of the proposed method is carried out. Thirdly, the processes of determination of the controlling parameters are shown. Furthermore, the dispersion characteristics of the proposed method are also investigated, and the maximum dispersion error of the proposed method can be decreased significantly. Finally, numerical experiments are presented to substantiate the efficiency of the proposed method.