Weakly conditionally stable finite-difference time-domain method

A novel weakly conditionally stable finite-difference time-domain (FDTD) method, which 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 one space discretisation and is presented analytically. Compared with the alternating-direction implicit (ADI) FDTD method, this new method has higher accuracy, especially for larger field variation rate and/or time-step size. By defining the field components at only two time steps, this new method requires the solution of four tridiagonal matrices and four explicit updates at each time step, which is more computationally efficient than the ADI-FDTD scheme. While maintaining the same size of time step, the CPU time for this method can be reduced to about 2/3 of that for the ADI-FDTD scheme. The numerical performance of the proposed method over the ADI-FDTD method is demonstrated through numerical examples.