Switchable Truncations Between the 1st- and 2nd-Order DZT-CFS-UPMLs for Relevant FDTD Problems

Abstract

Adopting the direct $Z$ -transform ( $\text{D}Z\text{T}$ ) method due to its higher accuracy instead of the approximate $Z$ -transform ( $\text{A}Z\text{T}$ ) methods and efficient and switchable truncations between the 1st- and 2nd-order uniaxial perfectly matched layers (UPMLs) with the complex-frequency-shifted (CFS) scheme are shown to terminate the relevant finite-difference time-domain (FDTD) regions. The proposed $\text{D}Z\text{T}$ -CFS-UPML formulations can possess the switchable function in terms of relevant FDTD problems so that the optimal performance can be obtained with the tradeoff among memory requirement, CPU time, and absorption accuracy. For the FDTD problem with the strong evanescent and weak low-frequency propagating waves, the proposed $\text{D}Z\text{T}$ -CFS-UPML formulations can be switched to the 1st-order PML truncation, and for the other cases with both low-frequency propagating and strong evanescent waves, the 2nd-order PML is the best choice. Two numerical simulations have been carried out to illustrate the validity and flexibility of the proposed approach.