A novel implementation for two‐dimensional unconditionally stable FDTD method

In this paper, a novel two‐dimensional unconditionally stable finite‐difference time‐domain (2D US‐FDTD) method based on the Crank–Nicolson (CN) scheme is proposed. In particular, in the proposed 2D 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 (with regards to time steps) as accurately as possible and (ii) only a single iteration that requires fewer 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. In particular, it is shown that the asymmetric effect (that is, the asymmetric result is obtained even for exactly symmetric computational setups), which always appears in the ADI‐FDTD algorithm, is not observed in the US‐FDTD method.