Efficient implementation of multi-pole UPML using trapezoidal approximation for general media

• The higher-order UPML based on the BZT for truncating FDTD domain is proposed.
• We model four 3D FDTD tests to validate the proposed formulations.
• The proposed PML based-BZT can set larger time step size than the one based-MZT.
• The proposed PML needs fewer steps than the published one in terms of given time.

Based on the uniaxial anisotropic perfectly matched layer (UPML) with multi-poles, unsplit-field implementation of the higher-order PML using the trapezoidal approximation (TA) method is proposed to terminate the finite-difference time-domain (FDTD) computational domains. From the point of view of the Courant–Friedrichs–Levy (CFL) condition, to the best of our knowledge, time step based on the TA only needs to meet CFL condition, whereas time step based on the matched Z-transform (MZT) method has to make it smaller for retaining stability and desirable accuracy. Moreover, these formulations are completely independent of the material properties of the FDTD domains and hence can be applied to truncate arbitrary media without any modification because of the D–B constitutive relations used in Maxwell's equations. Four numerical examples have been carried out in three dimensional (3D) FDTD computational domains to validate these formulations. It is shown that the proposed UPML formulations with two poles are effective in terms of attenuating both the low-frequency propagating waves and evanescent waves and reducing late-time reflections, and also can produce results as accurate as the published MZT-UPML but with fewer number of steps and less CPU time.