“…In order to overcome the CFL stability condition and improve computational efficiency, various implicit difference schemes have been adopted. Many implicit FDTD methods have been proposed, and all those methods show valuable performance improvement, such as hybrid implicit-explicit (HIE) FDTD method [3,4], Crank-Nicolson (CN) FDTD method [5,6], alternating-direction-implicit (ADI) FDTD method [7,8], locally-one-dimensional (LOD) FDTD method [9,10], and Weighted Laguerre Polynomial (WLP) FDTD method [11,12]. Among the implicit methods mentioned above, the HIE-FDTD method only applies implicit scheme to the spatial derivative in the direction along which there are fine elements, while taking general explicit scheme for the other spatial derivatives in the directions along which there are no fine structures.…”