An Efficient 3-D HIE-FDTD Method With Weaker Stability Condition

For analyzing the electromagnetic objects with the fine structures in one direction efficiently, a three-dimensional (3-D) hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method with weaker stability condition is proposed in this paper. First, by adopting the alternating-direction implicit (ADI) scheme, the 3-D Maxwell’s equations are subdivided into two substep procedures, and then by adding some disturbance terms into two substeps, respectively, the proposed method is derived. Compared with the existing HIE-FDTD methods, the Courant–Friedrichs–Lewy (CFL) stability condition of the proposed HIE-FDTD method is weaker, which means the proposed method is more efficient due to the possibility of choosing the larger time step size. In addition, the relationships between the CFL stability conditions and the numerical dispersion errors of the traditional FDTD method, the three HIE-FDTD methods, and the ADI-FDTD method are summarized in order to provide a basis for the choice among them.