Pinpoint and Efficient DZT-based FDTD Implementations Using Optimal 2nd-order PML Truncation

Abstract

Combining unsplit-field, D-B constitutive relations, and direct Z-transform method (DZT), efficient finite-difference time-domain (FDTD) formulations of the second-order perfectly matched layer (PML) based on the stretched coordinate (SC) scheme are proposed to model open domain problems. The proposed PML formulations can not only require less equations due to applying the unsplit-field implementation so that more CPU time and memory can be saved, but also be completely independent of properties of any materials due to using the D-B constitutive relations so that the open domain layered media problems can be solved. Besides, propagating and evanescent waves can be attenuated due to utilizing the multi-pole scheme which has the advantages of the conventional PML and the complex frequency-shifted PML (CFS-PML). Furthermore, the proposed DZT-based PML formulations can obtain higher absorption performance as compared with the published higher-order PML formulations based on the digital signal processing (DSP). The proposed method is validated using three numerical cases carried out in three dimensional (3D) dispersive layered media problems. It can be concluded from simulations results that the proposed formulations can not only absorb both the propagating and evanescent waves, but also hold higher absorption accuracy as compared with the published DSP-based PML formulations.