A novel three-dimensional unconditionally-stable FDTD method

A novel three-dimensional unconditionally-stable finite-difference time-domain (FDTD) method is presented, in which symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell´s equations into four sub-matrices. Accordingly, the time step is divided into four sub-steps. The normalized numerical phase velocity of the proposed method is better than that of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. In addition, the numerical dispersion error of the novel method is lower than that of the ADI-FDTD method. In order to demonstrate the efficiency of the proposed method, numerical results are presented. The saving in CPU time with the proposed method can be more than 30% in comparisons with the ADI-FDTD method and more than 69% in comparisons with the traditional FDTD method.