Efficient PML Implementation for Approximate CN-FDTD Method

Instead of applying the standard Crank-Nicolson (CN) method, an efficient perfectly matched layer (PML) based on the CN approximate-factorization-splitting (CNAFS) scheme is proposed to terminate three-dimensional (3-D) finite-difference time-domain lattices. It can not only be free from the Courant-Friedrich-Levy limit, but also has higher efficiency than the standard CN-PML. Considering that its iteration form based on the original CNAFS scheme is still complicated, its calculation speed is further improved via introducing a series of intermediate variables. All mathematical derivations are based on the bilinear transform method to guarantee the accuracy. Finally, the absorption performance, computational efficiency, and unconditional stability of our work are verified through two 3-D numerical examples of electromagnetic waves radiating in homogeneous spaces.