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

Int J RF Microw Comput Aided Eng

et al. 2021

The finite-difference time-domain (FDTD) algorithm shows disadvantages in bandpass signal simulation with fine structures along a single direction. The reason is that FDTD algorithm exists the Courant-Friedrichs-Levy (CFL) condition and bases on the lowpass-sampling theorem. Based on the numerical implementation, hybrid implicit-explicit procedure and complex envelope method are introduced. As a full-wave simulation method, higher order concept is incorporated into perfectly matched layer (PML) formulation for improving absorption at boundaries of the lattice. For unmagnetized plasma simulation, piecewise linear recursive convolution method is modified according to the bandpass signal. Through numerical example, the proposed algorithm shows considerable performance during the entire simulation which can be concluded from several aspects: (1) It takes advantages of higher order concept which shows enhanced absorption. ( 2) The proposed algorithm can overcome the CFL condition and maintain stability with the increment of time steps. (3) It shows considerable efficiency and accuracy in simulating structures with fine details along a single direction. (4) It can alleviate time increment problem among implicit algorithms with lower CFL numbers.

“…where ε ∞ is the infinite frequency permittivity, ν is the damping constant and ω p is the plasma frequency. 40 By substituting ( 4) into (5a)-(5b), equations can be reorganized as…”

Section: Theoretical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Wang²,

Int J RF Microw Comput Aided Eng

et al. 2021

“…In the CE method, the mesh size can be chosen according to the bandwidth rather than the maximum frequency, resulting in significantl improvement, both from the aspect of efficiency and accuracy. The CE method was firstly employed into the conventional FDTD algorithm [6]. Then, it was introduced into the unconditionally stable algorithms [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Narrow-Bandpass One-Step Leapfrog Hybrid Implicit-Explicit Algorithm with Convolutional Boundary Condition for Its Applications in Sensors

Wang

Jiang

et al. 2022

Sensors

A large number of sensors work in the narrow bandpass circumstance. Meanwhile, some of them hold fine details merely along one and two dimensions. In order to efficiently simulate these sensors and devices, the one-step leapfrog hybrid implicit-explicit (HIE) algorithm with the complex envelope (CE) method and absorbing boundary condition is proposed in the narrow bandpass circumstance. To be more precise, absorbing boundary condition is implemented by the higher order convolutional perfectly matched layer (CPML) formulation to further enhance the absorption during the entire simulation. Numerical examples and their experiments are carried out to further illustrate the effectiveness of the proposed algorithm. The results show considerable agreement with the experiment and theory resolution. The relationship between the time step and mesh size can break the Courant–Friedrichs–Levy condition which indicates the physical size/selection mesh size. Such a condition indicates that the proposed algorithm behaviors are considerably accurate due to the rational choice in discretized mesh. It also shows decrement in simulation duration and memory consumption compared with the other algorithms. In addition, absorption performance can be improved by employing the proposed higher order CPML algorithm during the whole simulation.

“…29 Due to the material-dependent PML formulation, existing schemes are unusable. 24,25,[30][31][32] Thus, the formulation must be modified for metamaterial simulation using the CN scheme.…”

mentioning

confidence: 99%

Narrow‐bandpass Crank–Nicolson algorithm with enhanced absorbing performance for metamaterials

Yue²,

Int J Numerical Modelling

et al. 2021

In this paper, an alternative algorithm for simulating metamaterials under a narrow bandpass condition is proposed. To calculate metamaterial regions with unique double negative property, the Drude model is used to solve the constitutive relationship. The effectiveness of the proposed algorithm over existing methods is demonstrated in terms of accuracy, efficiency, and simulation of absorption. For the numerical example, a metamaterial slab with a dipole antenna model is introduced. Compared with previous works, the numerical results indicate that the proposed algorithm is considerably efficient and simulates absorption. Most importantly, the algorithm can maintain stability and reduce simulation duration.