Development of the nearly PML for four-stages split-step unconditionally-stable FDTD method

An unconditionally-stable four-stages split-step nearly perfectly matched layer (PML) algorithm is presented for modeling open region finite-difference time-domain (FDTD) applications. The algorithm is based on incorporating the split-step scheme into the nearly PML approach. In the proposed method, symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell´s equations into four sub-matrices. Accordingly, the time step is divided into four sub-steps. The formulation of the proposed method is derived. Furthermore, numerical results are carried out at different positions for different Courant-Friedrichs-Lewy numbers in two-dimensional domains, which shown that the formulation is both accurate and unconditionally-stable.