A Novel 3-D Weakly Conditionally Stable FDTD Algorithm

For analyzing the electromagnetic problems with the fine structures in one or two directions, a novel weakly conditionally stable finite-difference time-domain (WCS-FDTD) algorithm is proposed. By dividing the 3-D Maxwell's equations into two parts, and applying the Crank-Nicolson (CN) scheme to each part, a four sub-step implicit procedures can be obtained. Then by adjusting the operational order of four sub-steps, a novel 3-D WCS-FDTD algorithm is derived. The proposed method only needs to solve four implicit equations, and the Courant-Friedrich-Levy (CFL) stability condition of the proposed algorithm is more relaxed and only determined by one space discretisation. In addition, numerical dispersion analysis demonstrates the numerical phase velocity error of the weakly conditionally stable scheme is less than that of the 3-D ADI-FDTD scheme.