Higher-order perfectly matched layer for the implicit CNDG-FDTD algorithm

On the basis of complex frequency-shifted perfectly matched layer (CFS-PML) formulation, an implementation of the higher-order PML is proposed to terminate unbounded finite-difference time domain (FDTD) computational domain. By incorporating the Crank-Nicolson Douglas-Gunn algorithm and the bilinear transform method, the proposed scheme can not only maintain the unconditional stability of the CN-FDTD algorithm in terms of reducing computational time but also take advantage of the higher-order PML in terms of improving absorbing performance. Numerical examples are provided to demonstrate the performance of the proposal in the homogenous free space and half-space soil vacuum problems, respectively. It is demonstrated that the proposed unconditionally stable higher-order CFS-PML can not only efficiently absorb low-frequency propagation waves, low-frequency evanescent waves, and late-time reflections but also overcome Courant-Friedrich-Levy limit.