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

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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Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions

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ENGINEERING ANALYSIS WITH boundary elementS 2017年 85卷 142-157页

作者： Liu, Cheng Chen, Leilei Zhao, Wenchang Chen, Haibo Univ Sci & Technol China Dept Modern Mech CAS Key Lab Mech Behav & Design Mat Hefei 230026 Anhui Peoples R China Xinyang Normal Univ Coll Civil Engn Xinyang 464000 Henan Peoples R China

This study presents an isogeometric fast multipole boundary element method (IGA FMBEM) in two-dimensional (2D) acoustics and a related sensitivity-based shape optimization algorithm for sound barriers. In the isogeometric analysis, Non-Uniform Rational B-Splines (NURBS) are used to accurately represent structural geometry. The control points are set as design variables in the shape optimization procedure given that their variations can flexibly result in shape changes. Acoustic shape sensitivities with respect to control points are calculated by the sensitivity boundary integral equation (BIE) based on the direct differentiation method. The singular integrals in the sensitivity BIEs are formulated explicitly under the isogeometric discretization. The minimization of sound pressure on the reference surface is selected as design objective. The gradient-based optimization solver is finally introduced for optimization iteration after the acoustic state and sensitivity information are obtained. The fast multipole method (FMM) is applied to improve overall computational efficiency. The Burton-Miller method is adopted to conquer the fictitious eigenfrequency problem in solving exterior acoustic problems. The correctness and validity of the proposed methods are demonstrated through a number of numerical simulations, while the performance of the sensitivity-based optimization algorithm is observed in the shape optimization of a 2D Gamma-shaped sound barrier. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Isogeometric analysis fast multipole boundary element method Acoustic shape sensitivity analysis Direct differentiation method Shape optimization

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Accuracy of the fast multipole boundary element method with quadratic elements in the analysis of 3D porous structures

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COMPUTATIONAL MECHANICS 2015年第3期56卷 477-490页

作者： Ptaszny, Jacek Silesian Tech Univ Inst Computat Mech & Engn PL-44100 Gliwice Poland

In this work, a fast multipole boundary element method for 3D elasticity problem was developed by the application of the fast multipole algorithm and isoparametric 8-node boundary elements with quadratic shape functions. The problem is described by the boundary integral equation involving the Kelvin solutions. In order to keep the numerical integration error on appropriate level, an adaptive method with subdivision of boundary elements into subelements, described in the literature, was applied. An extension of the neighbour list of boundary element clusters, corresponding to near-field computations, was proposed in order to reduce the truncation error of expansions in problems with high stress concentration. Efficiency of the method is illustrated by numerical examples including a solid with single spherical cavity, solids with two interacting spherical cavities, and numerical homogenization of solids with cubic arrangement of spherical cavities. All results agree with analytical models available in the literature. The examples show that the method can be applied to the analysis of porous structures.

关键词： fast multipole boundary element method Quadratic elements Porous materials Spherical cavities Homogenization

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A fast multipole boundary element method for Three-Dimensional Half-Space Acoustic Wave Problems Over an Impedance Plane

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2015年第1期12卷 1350090页

作者： Wu, Haijun Liu, Yijun Jiang, Weikang Lu, Wenbo Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Univ Cincinnati Cincinnati OH 45221 USA Shanghai Marine Equipment Res Inst Shanghai 200031 Peoples R China

A high-frequency fast multipole boundary element method (FMBEM) based on the Burton-Miller formulation is proposed for three-dimensional acoustic wave problems over an infinite plane with impedance boundary conditions. The Green's function for the sound propagation over an impedance plane is employed explicitly in the boundary integral equation (BIE). To deal with the integral appearing in the half-space Green's function, the downward pass in the FMBEM is divided into two parts to compute contributions from the real domain to the real and image domains, respectively. A piecewise analytical method is proposed to compute the moment-to-local (M2L) translator from the real domain to the image domain accurately. An algorithm based on the multi-level tree structure is designed to compute the M2L translators efficiently. Correspondingly, the direct coefficient can also be computed efficiently by taking advantage of the algorithm of the efficient M2L. A flexible generalized minimal residual (fGMRES) is applied to accelerating the solution when the convergence is very slow. Numerical examples are presented to demonstrate the accuracy and efficiency of the developed FMBEM. Good solutions and high acceleration ratios compared with the conventional boundary element method clearly show the potential of the FMBEM for large-scale 3D acoustic wave problems over an infinite impedance plane which are of practical significance.

关键词： fast multipole boundary element method impedance plane acoustic wave problems half-space domain

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Analyzing Acoustic Radiation Modes of Baffled Plates With a fast multipole boundary element method

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JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME 2013年第1期135卷 011007-011007-7页

作者： Wu, Haijun Jiang, Weikang Liu, Yijun Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Univ Cincinnati Cincinnati OH 45221 USA

In the analysis of an acoustic radiation mode of a baffled plate, Rayleigh integral with free space Green's function is involved. The boundary element method (BEM) is one of the approaches to compute its modes and radiation efficiencies. In this paper a fast multipole BEM in conjunction with an iterative solver based on the implicit restart Arnold method is proposed to efficiently and accurately evaluate acoustic radiation modes and efficiencies. Even though a 3D free space Green's function is used here, a quad tree is used for the hierarchical tree structure of the boundary mesh instead of an oct tree, which can speed up the fast multipole BEM. Similar to the analytical integration of moment evaluations, the analytical integration is also employed to compute the local expansion coefficients which further improves the efficiency of the fast multipole BEM for the analysis of an acoustic radiation mode of baffled plates. Comparison between numerical and theoretical radiation efficiencies of a baffled circular plate vibrating as a piston shows that the fast multipole BEM proposed here can give results with very good accuracy. The computation of the eigenvalues and eigenvectors of a baffled rectangular plate further reveals the efficiency in CPU time, smaller memory size, and accuracy of the fast multipole BEM in the analysis of an acoustic radiation mode. [DOI: 10.1115/1.4007023]

关键词： acoustic radiation modes fast multipole boundary element method baffled plates

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Prediction of Viscoelastic Behavior in Asphalt Concrete Using the fast multipole boundary element method

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JOURNAL OF MATERIALS IN CIVIL ENGINEERING 2013年第3期25卷 328-336页

作者： Zhu, Xing-yi Chen, Wei-qiu Yang, Zhong-xuan Shanghai Univ Shanghai Inst Appl Math & Mech Shanghai 200072 Peoples R China Zhejiang Univ Dept Engn Mech Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Dept Civil Engn Hangzhou 310058 Zhejiang Peoples R China

This paper describes an application of the fast multipole boundary element method (FMBEM) in simulating the viscoelastic behavior of asphalt concrete (AC). FMBEM has some merits including easy meshing of complicated geometries, accuracy in solving singular fields, high calculation efficiency, and low data storage requirements. These merits lead to many applications in multiple time-step and multi-inclusion problems, such as prediction of AC creep behavior. In this paper, a fast multipole formulation and an algorithm for two-dimensional linear viscoelastic problems are introduced first. To consider the bonding between the asphalt matrix and aggregates, a viscoelastic interface model is used to simulate the interfacial imperfection. A numerical model of asphalt concrete is then constructed based on image processing techniques, and the model is capable of taking into account the effects of the size and content of the air voids. The creep compliance of AC is predicted by the developed FMBEM arithmetic and subsequently compared with the experimental results. It has been shown that the developed method can describe and simulate the correct creep evolutionary trend of AC. DOI: 10.1061/(ASCE)MT.19435533.0000603. (C) 2013 American Society of Civil Engineers.

关键词： Asphalt concrete Micromechanics fast multipole boundary element method Viscoelastic properties Image processing technique

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3D ACOUSTIC SHAPE SENSITIVITY ANALYSIS USING fast multipole boundary element method

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2012年第1期9卷 1240004-1240011页

作者： Zheng, C. J. Chen, H. B. Matsumoto, T. Takahashi, T. Univ Sci & Technol China Dept Modern Mech Hefei 230027 Anhui Peoples R China Nagoya Univ Dept Mech Sci & Engn Nagoya Aichi 4648603 Japan

This paper presents a fast multipole boundary element approach to the 3D acoustic shape sensitivity analysis based on the discrete adjoint variable method. The Burton-Miller formula is used to conquer the fictitious eigenfrequency problem of the original boundary integral equation method in solving exterior acoustic problems. Constant elements are used to discretize the boundary, so that the hypersingular integrals contained in the formulae can be evaluated explicitly and directly. Numerical examples are presented to demonstrate the accuracy and efficiency of the present approach.

关键词： Acoustic shape sensitivity analysis adjoint variable method fast multipole boundary element method fictitious eigenfrequencies hypersingularity

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A new multi-level strategy of numerical integration in the fast multipole BEM for analyzing 3D potential problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2024年 161卷 174-189页

作者： Hu, Bin Li, Cong Niu, Zhongrong Anhui Univ Sci & Technol Sch Civil Engn & Architecture Huainan Peoples R China Anhui Jianzhu Univ Sch Civil Engn Hefei Peoples R China Hefei Univ Technol Sch Civil Engn Hefei Peoples R China

A multi-level strategy of numerical integration, incorporating Hammer-type quadrature, adaptive Gauss quadrature, and the improved semi-analytic method, is developed to evaluate the boundary integrals on triangular elements for three dimensional potential problems. The boundary integrals are classified into three categories according to the relative distance between the source point and the integral element. Hammer-type quadrature is used to evaluate the integrals on the element that is far from the source point, while adaptive..point Gauss quadrature is proposed to evaluate the integrals on the element that is closer to the source point, the number of quadrature points varies with the change of the relative distance. The improved semi-analytic method is proposed for the nearly singular integral on the element that is very close to the source point, where the conformal and sigmoidal transformations are introduced to mitigate the adverse effects caused by the distorted shape of the element. The effective ranges of Hammer-type quadrature and adaptive Gauss quadrature are investigated and a reasonable scheme for their activation is provided. The present multi-level strategy exhibits high accuracy, robustness, and efficiency for the integrals with 1/r, 1/r(3), and 1/r(5). It makes the fast multipole boundary element method more competitive and applicable in the analysis of large complex structures.

关键词： Multi-level strategy Nearly singular integral fast multipole boundary element method 3D potential problem

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Three-dimensional numerical investigation on propagation characteristics of road traffic noise from an embankment road: Construction of correction formula for the effect of side slope angle

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ACOUSTICAL SCIENCE AND TECHNOLOGY 2024年第4期45卷 184-194页

作者： Yasuda, Yosuke Nishimura, Seiya Kamiya, Yu Morinaga, Makoto Kanagawa Univ Fac Architecture & Bldg Engn 3-27-1 Rokkakubashi Yokohama Kanagawa 2218686 Japan Kanagawa Univ Fac Engn 3-27-1 Rokkakubashi Yokohama Kanagawa 2218686 Japan Kanagawa Univ Grad Sch Engn 3-27-1 Rokkakubashi Yokohama Kanagawa 2218686 Japan Kumagai Gumi Co Ltd Tech Res & Dev Inst 1043 Onigakubo Tsukuba 3002651 Japan

Through three-dimensional wave-based numerical analysis, the propagation characteristics of road traffic noise from embankment roads were investigated, focusing on the effects of the side slope angle and height of the embankment. When the prediction plane was set as an orthogonal cross-section in the lane direction, the distribution of A-weighted sound pressure level differences between embankments with a slope and a right-angle wedge showed relatively high values in the region corresponding to the paths where diffracted sound from the edge of the embankment reflects off the ground surface, regardless of the embankment height, slope angle, and position of the prediction plane. When the embankment height and slope angle were the same, the level difference distribution was nearly the same regardless of the position of the sound source and orthogonal prediction plane. Based on these characteristics, an empirical correction formula was proposed, applicable to an arbitrary orthogonal cross-section to the embankment lane direction, representing the effect of the embankment slope angle in terms of the A-weighted sound pressure level difference. By appropriately setting the values of the coefficients required in the formula, both the maximum and average errors in the prediction plane can be reduced without significantly amplifying either of them.

关键词： Road traffic noise Diffraction Embankment Wave-based numerical analysis fast multipole boundary element method

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A fast multipole boundary element method Based on Legendre Series for Three-dimensional Potential Problems

A Fast Multipole Boundary Element Method Based on Legendre S...

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3rd International Conference on Manufacturing Science and Engineering (ICMSE 2012)

作者： Yu, Chunxiao Yu, Haiyuan Chen, Yiming Yanshan Univ Coll Sci Qinhuangdao Peoples R China

ISBN: (纸本)9783037853696

Vectorization expressions of a fast multipole boundary element method (FM-BEM) based on Legendre series are presented for three-dimensional (3-D) potential problems. The formulas are applied to the expression of fundamental solutions for the boundary element method(BEM). Truncation errors of the multipole expansion and local expansion are deduced and analyzed. It shows that the errors can be controlled by truncation terms.

关键词： fast multipole boundary element method Legendre series Potential problems

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