Accurate and computationally efficient two-dimensional unconditionally stable FDTD method

In this paper, an accurate and computationally efficient two-dimensional unconditionally stable finite-difference time-domain (2-D US-FDTD) method based on the Crank-Nicolson scheme is proposed. In particular, in the proposed 2-D US-FDTD method the field components are defined at only two time steps n and n+1; and the original time-dependent Maxwell's equations of the Crank-Nicolson scheme are solved by introducing a proper intermediate value for a field component. Compared to the ADI-FDTD method, the US-FDTD method offers the following two advantages: i) the left-hand and right-hand sides of the original updating equations are balanced (in respect of time step) as much accurate as possible and, ii) only a single iteration that requires less number of updating equations is needed for the field development. The numerical performance of the proposed US-FDTD method over the ADI-FDTD algorithm is demonstrated through numerical examples.