An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation

Decleer, Pieter; Londersele, Arne Van; Rogier, Hendrik; Ginste, Dries Vande

doi:10.1016/j.cam.2021.113881

Cited by 7 publications

(9 citation statements)

References 74 publications

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“…e first step is to discretize space and time by dissecting the xt plane into a grid, where the x and t coordinates are divided into m and n equal parts; here, we have Δx � h � l/m, directional increment k � Δt, where l is the thickness of the specialized protective clothing fabric material layer, while we let i denote the position x transverse axis and j denote the transverse axis position t, with each grid point in the grid corresponding to one of its temperature values. Figure 2 shows the node diagram of the discrete post-finite difference manifold [18]. us, the temperature of the outer side of the dummy skin can be easily known in relation to the different thickness layers and the temperature distribution.…”

Section: Finite Difference Methods For Solving the One-dimensionalmentioning

confidence: 99%

“…In equation (18), K is the Boltzmann constant, T is the current absolute temperature, and P(Δf) is the probability of accepting the new state solution. At this point, there exists a random number c ∈ [0, 1], if P(Δf) > c, the new state arrangement is accepted; if P(Δf) ≤ c, the original state arrangement is retained.…”

Section: Study On the Optimization Model Of The Thickness Of Protecti...mentioning

confidence: 99%

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Study on Heat Transfer Characteristics and Intelligent Optimization of Protective Clothing Materials in front of the Blast Furnace

Duan

et al. 2022

Computational Intelligence and Neuroscience

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Special protective clothing should have a certain thermal insulation and protective effect in the production in front of the blast furnace. In order to study the design of special protective clothing for blast furnace foreman, its temperature distribution and internal thickness structure are deeply analyzed. First, based on the existing experimental data, combined with heat transfer and the Fourier law theory, a one-dimensional unsteady heat conduction equation is established. Using the explicit finite difference solution algorithm, the distribution law of the temperature of each fabric layer with time is obtained and the error analysis is performed. The error result is 0.42877%, which shows that the numerical solution is stable and convergent. Then, through the intelligent optimization model of a simulated annealing ant colony (SA-ACO), compared with the single ant colony algorithm (ACO) and a simulated annealing algorithm (SA), it avoids falling into the local optimal solution, reversely solves the optimal thickness of two layers of protective clothing in front of the blast furnace, improves the convergence speed of optimization, and verifies the reliability of the model with a sensitivity test. Finally, this paper actually solves the problem of the protective clothing design and mathematical intelligent model in front of the blast furnace and combines it with numerical simulation software to realize the numerical simulation of temperature distribution and thickness optimization of special protective clothing in front of the blast furnace, so as to provide theoretical guidance for enterprise blast furnace production and development of special protective clothing.

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Section: Finite Difference Methods For Solving the One-dimensionalmentioning

confidence: 99%

Section: Study On the Optimization Model Of The Thickness Of Protecti...mentioning

confidence: 99%

Study on Heat Transfer Characteristics and Intelligent Optimization of Protective Clothing Materials in front of the Blast Furnace

Duan

et al. 2022

Computational Intelligence and Neuroscience

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“…Consequently, the system can be solved using the tridiagonal matrix algorithm as explained in [17], such that the complexity remains of linear order O(n) [33]. In Appendix B, the update scheme ( 16) is given in a more accessible scalar notation.…”

Section: B Electromagnetic Potentialsmentioning

confidence: 99%

“…The FDTD method is also popular in computational QM and has been applied to the Schrödinger or Kohn-Sham equations with many variations [9]- [14]. Implicit schemes such as [15], [16] have been recently improved by also including local implicitization [17]. Many implementations exist that couple the EM and QM problems [18]- [21], where, depending on the problem at hand, an effective-mass Schrödinger equation [22]- [26] or the ab initio Kohn-Sham equation [27]- [30] is considered.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid EM/QM Framework Based on the ADHIE-FDTD Method for the Modeling of Nanowires

Decleer

Ginste

2022

IEEE J. Multiscale Multiphys. Comput. Tech.

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A new modeling formalism to compute the timedependent behavior of combined electromagnetic (EM) and quantum mechanical (QM) systems is proposed. The method is geared towards highly multiscale geometries, which is vital for the future design of nanoelectronic devices. The advocated multiphysics modeling formalism leverages the alternating-direction hybrid implicit-explicit (ADHIE) finite-difference time-domain (FDTD) method for the EM fields and is combined with a novel ADHIE method for the EM potentials. Additionally, we tackle the QM problem using a new split real and imaginary part formulation that includes higher-order spatial differences and arbitrary timedependent EM potentials. The validity of the proposed formalism is theoretically discussed by deriving its stability condition and calculating the numerical dispersion relation. Furthermore, the applicability of our modeling approach is proven through several numerical experiments, including a single-particle Maxwell-Schrödinger (MS) system as well as a many-particle Maxwell-Kohn-Sham (MKS) system within the time-dependent density-functional theory (TDDFT) framework. These experiments confirm that the novel ADHIE method drastically decreases the computation time while retaining the accuracy, leading to efficient and accurate simulations of light-matter interactions in multiscale nanoelectronic devices.

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“…Considering the components of the PIC, an optical switch is an important element that can work analogous to the electronic transistor in the electronic integrated circuits. Therefore, utmost efforts are made to achieve the functions of optical switching element using the time domain [16] or frequency domain [17], with different topologies in the form of cross waveguide geometries [18], quantum dots [19], optoelectronic hybrid devices [20], ring resonators [21], combined configurations of thermodynamics and optical components [22] and utilization of transparent and active materials [23,24], with it desired working and implementation in the optical circuits. A 2D-FDTD design of an optical switch is investigated in [25], by means of the phenomenon of GMR with varying radius cavity implemented at the start of the PhC-mesh.…”

Section: Introductionmentioning

confidence: 99%

A 3-Dimensional Modelling of the Optical Switch Based on Guided Mode Resonances in Photonic Crystals

Rehman¹,

Khan²,

Irfan³

et al. 2023

Preprint

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Optical switching is an essential part of photonic integrated circuits and the focus of research at the moment. In this research, an optical switch design working on the phenomenon of the guided-mode resonances in 3D photonic crystals-based structure is reported. The optical-switching mechanism is studied in a dielectric slab-waveguide-based structure operating in the near-infrared range in a telecom window of 1.55 µm. The mechanism is investigated by interference of two signals, i.e., the data signal and the control signal. The data signal is coupled into the optical structure and filtered utilizing guided-mode resonance, whereas, the control signal is index guided in the optical structure. The amplification or de-amplification of the data signal is controlled by tuning the spectral properties of the optical sources and structural parameters of the device. The parameters are optimized first using a single-cell model with periodic boundary conditions and later in a finite 3D-FDTD model of the device. The numerical design is computed in an open-source Finite Difference Time Domain simulation platform. Optical amplification in the range of 13.75 % is achieved in the data signal with a decrease in the linewidth up to 0.0079 µm and a quality factor of 114.58. The proposed device presents great potential in the field of photonic integrated circuits, biomedical technology, and programmable photonics.

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An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation

Cited by 7 publications

References 74 publications

Study on Heat Transfer Characteristics and Intelligent Optimization of Protective Clothing Materials in front of the Blast Furnace

Study on Heat Transfer Characteristics and Intelligent Optimization of Protective Clothing Materials in front of the Blast Furnace

A Hybrid EM/QM Framework Based on the ADHIE-FDTD Method for the Modeling of Nanowires

A 3-Dimensional Modelling of the Optical Switch Based on Guided Mode Resonances in Photonic Crystals

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