A Novel WCS-FDTD Method With Weakly Conditional Stability

A novel weakly conditionally stable finite-difference time-domain (FDTD) method that is extremely useful for problems with very fine structures over a large computational domain in one or two directions is presented. The time step in this method is only determined by the largest space discretization. The weakly conditional stability and the dispersion relation of the proposed novel weakly conditionally stable (NWCS)-FDTD method are presented analytically. Compared with the alternating-direction implicit (ADI)-FDTD method, this NWCS-FDTD method has higher accuracy, especially for larger time-step size. At each time step, the NWCS-FDTD method requires the solution of four tridiagonal matrices and four explicit updates. While maintaining the same size of the time step, the CPU time for this weakly conditionally stable FDTD method can be reduced to about two-thirds of that for the ADI-FDTD scheme. The numerical performance of the proposed NWCS-FDTD method over the ADI-FDTD method is demonstrated through numerical examples.