Analysis of iterated ADI-FDTD schemes for Maxwell curl equations

The convergence of the iterative ADI-FDTD method proposed by Wang et al. [S. Wang, F. Teixeira, J. Chen, An iterative ADI-FDTD with reduced splitting error, IEEE Microwave Wireless Comp. Lett. 15 (2005) 1531–1533] towards the classical implicit Crank–Nicolson scheme when applied to Maxwell curl equations, and the accuracy, stability, and dispersion properties of the resulting iterated schemes are investigated. The iterated schemes are shown both mathematically and numerically to be unconditionally stable for 2D wave problems, in agreement with numerical experiments conducted in [S. Wang, F. Teixeira, J. Chen, An iterative ADI-FDTD with reduced splitting error, IEEE Microwave Wireless Comp. Lett. 15 (2005) 1531–1533]. However these schemes lose their unconditional stability when applied to full 3D wave problems where TE and TM modes do not decouple, as illustrated by numerical experiments in a PEC box.