Efficient unconditionally stable one-step leapfrog ADI-FDTD method with low numerical dispersion

An efficient unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method based on the controlling parameters is presented. First, three controlling parameters are introduced to the matrices of the Maxwell's equations to decrease the numerical dispersion error, and then the formulation of an efficient one-step leapfrog ADI-FDTD method is derived. Second, the analysis shows that the proposed method is unconditionally stable. Moreover, the numerical dispersion relation of the proposed method is derived analytically. Third, the process of determination of the controlling parameters is shown. Furthermore, the effects of the propagation angle, mesh size, time step and frequency on the dispersion characteristics of the proposed method are also investigated. The result shows that the normalised numerical phase velocity error (NNPVE) and maximum NNPVE of the proposed method are decreased significantly. Finally, two numerical examples are simulated to demonstrate the accuracy and efficiency of the proposed method.