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Extension of the contour-path effective-permittivity finite-difference time-domain method to three-dimensional problems for the analysis of arbitrarily shaped dielectric media

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2023年第12期65卷 3113-3119页

作者： Takeya, Kazuma Iwamoto, Tetsuya Shibayama, Jun Yamauchi, Junji Nakano, Hisamatsu Hosei Univ Fac Sci & Engn 3-7-2 Kajino Cho Koganei Tokyo 1848584 Japan

The conventional finite-difference time-domain (FDTD) method has been formulated in the Cartesian coordinate system. In this case, the staircase approximation should be used even for the analysis of arbitrarily shaped dielectric media. As a result, small meshes are required to accurately model these media. In this letter, we extend the contour-path effective-permittivity (CP-EP) technique to three-dimensional (3D) problems in which a reasonably accurate solution can be obtained with larger meshes for arbitrarily shaped dielectric media. The formulation is performed with the position of the dielectric medium being considered in each cell, leading to its effective permittivity. We compare the result from the present method with the Mie solution and that from the conventional staircase FDTD method to confirm the effectiveness of the 3D CP-EP technique. The relative error of the scattering cross-section is reduced to about half that of the staircase FDTD method.

关键词： arbitrarily shaped dielectric media contour-path effective-permittivity technique finite-difference time-domain method Mie solution staircase approximation

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Computationally efficient transparent sound source for the finite-difference time-domain method

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ACOUSTICAL SCIENCE AND TECHNOLOGY 2023年第5期44卷 371-382页

作者： Toyoda, Masahiro Yatabe, Kohei Kansai Univ Fac Environm & Urban Engn Dept Architecture 3-3-35 Yamate Cho Suita 5648680 Japan Tokyo Univ Agr & Technol Fac Engn Dept Elect Engn & Comp Sci 2-24-16 Naka Cho Koganei 1848588 Japan

The standard acoustic finite-difference time-domain methods often employ a transient input waveform as a sound source and introduce the waveform into an update equation of the sound pressure. There are three techniques to introduce the waveform: hard source, soft source, and transparent source. In the present paper, the advantages and disadvantages of these three techniques are firstly illustrated. Although the transparent source is most appropriate for obtaining an impulse response, an existing approach to achieve the transparent source requires heavy precomputation. To overcome this issue, the present paper proposes a computationally efficient approach for introducing the transparent source. It is derived from a mathematical investigation of the relation between an input source signal and the excited wave field. To validate the proposed approach, simple sound fields where diffraction effects can be ignored are considered, and the numerical results of the proposed approach are compared with those of the geometrical prediction. Furthermore, the proposed approach is applied to one-and two-dimensional situations for comparison with the existing methods. Computational efficiency of the proposed approach is shown, and some discussions on the difference of excited sound fields are provided.

关键词： finite-difference time-domain method Sound source Transparent source Green's function

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A One-Dimensional Electronic Fluid Model Based on the finite-difference time-domain method 14

A One-Dimensional Electronic Fluid Model Based on the Finite...

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14th International Symposium on Antennas Propagation and EM Theory

作者： Wang, Yuansu Bo, Yong Yang, Lixia Anhui Univ Sch Elect & Informat Engn Hefei Peoples R China

ISBN: (纸本)9798350353129;9798350353136

The breakdown of gas by high-power microwaves generates plasma, which significantly impacts the propagation of these microwaves. Consequently, investigating the atmospheric propagation of high-power microwaves is of paramount importance. This study employs an electron fluid model, integrating additional models to explore the interaction between high-power microwaves and gas plasma. The paper presents the difference equations of the one-dimensional electron fluid model, which are numerically solved using the finite-difference time-domain (FDTD) method. To validate the efficacy of this algorithm, the simulated air breakdown threshold is compared with experimental data, revealing a strong correlation between the two.

关键词： High power microwave gas breakdown electron fluid model electron energy distribution function finite-difference time-domain method particle simulation

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Nonlinear finite-difference time-domain method for exciton-polaritons: Application to saltatory conduction in polariton neurons

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Physical Review B 2024年第21期110卷 214303-214303页

作者： K. Dini H. Sigurðsson N. W. E. Seet P. M. Walker T. C. H. Liew Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore Institute of Experimental Physics Faculty of Physics University of Warsaw ul. Pasteura 5 PL-02-093 Warsaw Poland Science Institute University of Iceland Dunhagi 3 IS-107 Reykjavik Iceland School of Mathematical and Physical Sciences University of Sheffield S3 7RH Sheffield United Kingdom

Recently emerging complex photonic structures exhibiting giant optical nonlinearity through strong light-matter coupling require new theoretical approaches to accurately capture the interplay of the photonic and interacting-matter degrees of freedom. Extending the finite-difference time-domain method, we develop an algorithm for solving the nonlinear Maxwell-Bloch equations. This allows first-principles modeling of exciton-polariton systems for arbitrarily complex photonic structures with photon-exciton coupling and frequency dependent nonlinear response included without approximations or phenomenological parameters. We first validate the algorithm by reproducing the bistable hysteresis cycle of polaritons in the nonlinear regime. We then give a key example of its utility by simulating polariton dynamics in integrated photonic circuitry composed of spatially localized bistable nodes connected by high speed waveguides. We propose a polariton circuit element inspired by saltatory conduction in biological neurons. This design supports faster polariton signal propagation than previous designs, however, requires a full account of the nonlinear field distributions in both propagation and growth directions to be calculated.

关键词： Exciton polariton First-principles calculations Semiconductor microcavities finite-difference time-domain method

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Benchmarking of finite-difference time-domain method and fast multipole boundary element method for room acoustics

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APPLIED ACOUSTICS 2022年 191卷 108662-108662页

作者： Li, Yue Meyer, Julie Lokki, Tapio Cuenca, Jacques Atak, Onur Desmet, Wim Siemens Digital Ind Software Interleuvenlaan 68 B-3001 Leuven Belgium Aalto Univ Dept Comp Sci Konemiehentie 29 FI-02150 Espoo Finland Aalto Univ Dept Signal Proc & Acoust Maarintie 8 FI-02150 Espoo Finland Katholieke Univ Leuven Dept Mech Engn Celestijnenlaan 300 B-3001 Heverlee Belgium Flanders Make DMMS Core Lab Lommel Belgium

Compared to geometrical acoustics, wave-based methods which solve the wave equation either in the time domain or in the frequency domain are known for their high accuracy. However, their systematic use as professional room acoustic simulation tools is less popular due to the modelling effort and com-putational time requirements, especially in the case of complex scenarios. This paper aims at providing guidelines for the use of two wave-based methods in complex room acoustics simulations, namely the finite-difference time-domain (FDTD) method and the fast multipole boundary element method (FMBEM). Numerical experiments are conducted to address the convergence issues of the two solvers, more specifically, the selection of the convergence tolerance of the iterative solver in FMBEM and the temporal sampling frequency in FDTD. To evaluate the capability of the solvers in simulating complex scenarios, five cases with increasing complexity of material input data are presented. The results show that both solvers give close predictions for various room acoustics parameters. In addition, an uncertainty sensitivity study is performed in a case where experimental data is available. Large deviations between measured and simulated reverberation time reveal that typical material data-sets poorly represent the behaviour of real materials in a room acoustics context. Lastly, the efficiency of the two solvers is dis-cussed. With parallelization implemented, both solvers can simulate sizeable room acoustic problems with good accuracy within a reasonable time. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： room acoustic simulation uncertainty finite-difference time-domain method fast multipole boundary element method

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Numerical solution of the Schrodinger equation in polar coordinates using the finite-difference time-domain method

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JOURNAL OF COMPUTATIONAL ELECTRONICS 2020年第1期19卷 91-102页

作者： Salehi, Mohsen Granpayeh, Nosrat KN Toosi Univ Technol Ctr Excellence Electromagnet Fac Elect Engn Tehran Iran

In quantum mechanics, many concepts, equations, and interactions are expressed as functions of the radius and angles and are therefore best understood and handled directly in polar or spherical coordinates. A finite-difference time-domain (FDTD) method for solving the two-dimensional Schrodinger equation in polar coordinates is proposed herein. In this method and through a subgridding approach, new nodes are added on rings far from the origin to retain the precision of the mesh grids;then a trigonometric interpolation is used to calculate the derivatives at these nodes. A comparison with analytic solutions for a two-dimensional (2D) harmonic oscillator is carried out to verify the performance of the code. A simple method based on the spatial Fourier transform is presented for the separation of degenerate eigenstates. A 2D quantum dot is also simulated and analyzed. When using this polar FDTD method along with proposed subgridding approach, the resolution of the solutions and Hamiltonian terms are conserved in the whole space of a plane of polar coordinates, and all operators or results expressed in polar coordinates can be easily implemented or obtained.

关键词： finite-difference time-domain method Schrodinger equation in polar coordinates Harmonic oscillator Quantum dot Degenerate states

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finite-difference time-domain method For Room Acoustic Simulation - Auralization And Applications

Finite-Difference Time-Domain Method For Room Acoustic Simul...

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作者： Jukka Saarelma Aalto University

学位级别：博士

Room acoustic simulation have been a practical tool in the design of acoustic spaces for several decades. More recently common prediction methods have been optimized and increasingly applied to real-time systems such as virtual reality and augmented reality applications. Modern computing hardware has made approaches that were previously too computationally intensive applicable for wide bandwidth simulation.Â Wave-based methods, and especially time-domain solvers for scalar wave equation have gained increasing attention for the use in room acoustic simulation. One of the methods, the finite-difference time-domain method has been proposed as a potential candidate due to convenient scalability properties and the parallel nature of the explicit forms of the method. However, the finite-difference time-domain method has several problematic properties that limit its usage. Due to its direct discretization approach, the dispersion relation in the numerical domain is anisotropic and nonlinear, thus resulting in dispersive wave propagation. Although the properties of the method have been well studied, the implications for its use in auralization have received limited attention.Â This thesis studies the numerical error involved in the finite-difference time-domain method within the context of auralization. The absolute thresholds of dispersion error are measured for several different explicit finite-difference schemes as well as under different acoustic conditions. Additionally the method is studied in terms of its application for real-time auralization and analysis of modal time evolution in room acoustics.Â The results indicate that the audibility of the dispersion error is dependent on simulation distance, which determines the amount of the accumulated group delay error in the simulation result. The group delay error is masked inaudible by the absorption of air when the phase velocity error is less than 0.28%. Early reflections are shown to further mask the dispersion er

关键词： finite-difference time-domain method auralization room acoustics aikatason differenssimenetelmä auralisaatio huoneakustiikka

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Moving sound source with an arbitrary trajectory in the two-dimensional finite-difference time-domain method

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JAPANESE JOURNAL OF APPLIED PHYSICS 2021年第SD期60卷

作者： Tsuchiya, Takao Kanamori, Masashi Doshisha Univ Dept Informat Syst Design Kyoto 6100321 Japan Japan Aerosp Explorat Agcy Chofu Aerosp Ctr Chofu Tokyo 1828522 Japan

In this paper, a moving sound source with an arbitrary trajectory is implemented using the finite-difference time-domain (FDTD) method. Two methods are proposed for implementing a moving-point sound source in the FDTD method, in which physically valid analysis is possible, including that of the Doppler effect. One method is the direct method and the other is the convolution method. We produce formulations and perform numerical experiments for a two-dimensional sound field, and the accuracies of the two proposed methods are compared. It is confirmed that both methods can be applied to a moving sound source, including the Doppler effect, and that the two methods have almost the same accuracy. It is found that the convolution method has advantages in that the source waveform and speed of movement can be freely changed at the time of convolution.

关键词： finite-difference time-domain method moving sound source Doppler effect convolution method

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Numerical investigation of the sound-insulation effect of a suspended ceiling structure with arrayed Helmholtz resonators by the finite-difference time-domain method

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APPLIED ACOUSTICS 2021年 172卷 107601-107601页

作者： Asakura, T. Tokyo Univ Sci 2641 Yamazaki Noda Chiba 2780022 Japan

In order to develop a numerical simulation of floor impact sound transmission via a floor structure that includes sound absorption materials, floor impact sound transmission via a composite floor structure composed of concrete slab, suspended ceiling plate, and an array of Helmholtz resonators inside a sand-wiched air layer is modeled by the discrete wave-based numerical method of the vibroacoustic finite-difference time-domain (FDTD). As a preliminary study, the reverberant sound absorption coefficients of absorbers that contain arrayed resonators are simulated and compared to empirically measured values. The accuracy of the estimated sound absorption coefficient is found to depend largely on the diffuseness of the sound field in the simulated sound field as well as in reality. Thereafter, the floor impact sound generated by a floor structure that contains an array of resonators inside a sandwiched air layer between the floor slab and the ceiling plate is simulated, and relatively good agreement between the calculated and measured results for the improvement of the impact sound pressure levels caused by the installation of the resonators was confirmed. This suggests the applicability of the vibroacoustic FDTD method to sound-insulation prediction of the floor impact sound. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： finite-difference time-domain method Reverberation room method Impact vibration Floor impact sound

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Fast method for analysing nonlinear composite right/left-handed transmission lines based on finite-difference time-domain method

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IET MICROWAVES ANTENNAS & PROPAGATION 2019年第2期13卷 127-133页

作者： Kouhpayeh-Zadeh-Esfahani, Sedigheh Abdipour, Abdolali Afrooz, Kambiz Amirkabir Univ Technol Microwave Mm Wave & Wireless Commun Res Lab Elect Engn Dept Tehran Polytech 424 Hafez Ave Tehran Iran Shahid Bahonar Univ Kerman Microwave & Millimeter Wave Res Grp Elect Engn Dept 22 Bahman Ave Kerman Iran

In this study, a new finite-difference time-domain (FDTD) scheme is presented for analysing nonlinear composite right/left-handed (CRLH) transmission lines, with reduction of the central processing unit time. A step by step analysis is demonstrated to solve the equations for nonlinear CRLH transmission lines based on the FDTD method. The proposed method is applied to a nonlinear CRLH transmission line as an example and the results are confirmed by those of the conventional FDTD method. The comparisons reveal that the presented solution efficiently decreases by about 82% of the computational time consumption.

关键词： telecommunication transmission lines finite difference time-domain analysis computational complexity transmission line theory nonlinear composite right-left-handed transmission lines nonlinear CRLH transmission lines finite-difference time-domain method FDTD method central processing unit time reduction computational time consumption

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