Implementation of the Crank‐Nicolson Douglas‐Gunn finite‐difference time domain with complex frequency‐shifted perfectly matched layer for modeling unbounded isotropic dispersive media in two dimensions

Abstract

AbstractTo model open‐domain problems with Drude, Lorentz, and Debye media, the complex frequency‐shifted perfectly matched layer (CFS‐PML) is adopted to truncate the Crank‐Nicolson Douglas‐Gunn finite‐difference time‐domain (CNDG‐FDTD) region. The auxiliary differential equation (ADE) and the bilinear Z‐transform methods are incorporated separately into the implementations of CNDG‐CFS‐PML formulations, while the ADE, piecewise linear recursive convolution (RC), and trapezoidal RC methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but also have the advantages of the CFS‐PML in attenuating the evanescent waves and reducing the late‐time reflection. Three numerical examples have been carried out to validate these formulations. The simulation results show that the proposed CNDG‐CFS‐PML algorithm is efficient in absorbing performance and saving more computational time compared with the conventional FDTD method, which leads to extensive applicability and acts as a very good prospect.