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

To 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 (BZT) methods are incorporated separately into the implementations of CNDG-CFS-PML formulations, while the ADE, piecewise linear recursive convolution (PLRC), and trapezoidal recursive convolution (TRC) methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but 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.

Bandpass signal formulation with hybrid implicit‐explicit procedure in open regions for unmagnetized plasma

“…[49][50][51] However, they cannot be directly extended to three-dimensions. 52 Recently, higher order convolutional PML is carried out for unmagnetized simulation. 53 The CE method is introduced into unconditionally stable schemes in References 38,39 and 40.…”

A nonconforming SO‐DGTD method with local time‐stepping for the simulation of nanophotonic

“…In the nanophotonics simulation, the Drude or Drude-Lorentz model is the common dispersion model for characterizing the plasmon behavior of metal materials, and they have been coupled with numerical methods and used in the time domain electromagnetic analysis. 1,2 There are varieties of numerical methods for solving time-domain Maxwell equations, such as the finite-difference time domain method (FDTD), 3 the time-domain finite volume method (FVTD), 4 the time-domain finite element method (FETD), 5 and the discontinuous Galerkin time-domain method (DGTD). 6 Among these methods, the DGTD method is especially suitable for solving electromagnetic problems with complex structures due to the flexibility of its mesh discretization, high order accuracy, and explicit time marching.…”

Complex Envelope Approximate Crank-Nicolson Method and Its Open Boundary Implementation for Bandpass Problem

“…Thus, a series of approximate CN algorithms are developed in two-dimensions, such as CN approximate-decoupling and CN Douglas-Gunn [13][14]. It should be noticed that the approximate CN algorithms in 2-D cases cannot be expanded to 3-D cases directly [15]. Recently, CN cycle-sweep (CS), CN approximatefactorization-splitting (AFS) and CN direct-splitting (DS) schemes are introduced to three-dimensions [16][17].…”