Direct $Z$ -Transform Implementation of the CFS-PML Based on Memory-Minimized Method

Efficient and unsplit-field-based stretched coordinate perfectly matched layer (PML) formulations with the complex frequency-shifted (CFS) scheme that combine the memory-minimized method (Tri-M) and the direct Z-transform (DZT) method are proposed to truncate the finite-difference time-domain lattices. The proposed algorithm takes advantage of the minimized memory of the Tri-M method, the optimal accuracy of the DZT method, and the capacity of the PML for attenuating evanescent waves and reducing late-time reflections. Three 3-D numerical simulations have been carried out to validate the proposed formulations.