A novel separable backward-central finite difference time domain (FDTD) method

In this paper, we present a novel, separable, backward-central FDTD (SBC-FDTD) method in which both the backward and central differencing are employed to discretize the time and spatial derivatives of the Maxwell´s equations. For the type of problems in which the FDTD cell size in one direction is much smaller than those along the other directions, the time step in the proposed SBC-FDTD technique can be determined by the largest cell size instead of the smallest one in the conventional Yee-FDTD. Though not as unconditionally stable as the alternating-direction implicit FDTD (ADI-FDTD), it has the advantage of being implicit in only one direction along which the time step is increased beyond the Courant condition. Both the numerical experiments and stability property have demonstrated that the proposed scheme is stable and accurate. A two dimensional cavity has been used to validate the proposed technique.