On the BEM for acoustic wave problems

Liu, Yijun

doi:10.1016/j.enganabound.2019.07.002

Cited by 59 publications

(22 citation statements)

References 106 publications

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“…Consider the propagation of time-harmonic acoustic waves in the domain Ω c exterior to a closed bounded domain Ω ⊂ R 3 The domain Ω c is filled with homogeneous and isotropic acoustic medium. The problem is governed by the well-known Helmholtz equation…”

Section: Problem Statementmentioning

confidence: 99%

“…By contrast, the high frequency FMM can enhance the upper limit of the computable frequency by increasing the number of the degree of freedoms (DOFs), at which acceptable results can be obtained in a reasonable time. As stated in Reference 3, however, although the recent research progress on the FMMs assures that it is now possible to simulate acoustic BEM problems with up to a few million DOFs within a few hours on a PC, the mentioned‐above upper limit of the frequency (nondimensional wavenumber) is generally still fairly small. Therefore, the FMM is generally only suitable for low and mid frequency problems.…”

Section: Introductionmentioning

confidence: 99%

“…Most of them restrict their applications to either a small number of elements or flat elements with constant values of variables, rendering them ineffective for some problems, especially at a high frequency. As stated in Reference 3, in the last decade, the use of constant elements with the dual boundary integral equation (BIE) formulation has become a common practice in the research of the acoustic BEM, especially with the fast solution methods. This is mainly caused by the hypersingularity involved in dual BIE formulation.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical analysis of high-frequency acoustic problems plays a crucial role in science and engineering fields, such as the radiation dose measurement, electromagnetic pulse damage, and underwater sonar imaging detection. [1][2][3] However, it is difficult to effectively solve exterior acoustic problems with large wavenumber due to the oscillatory behavior of the solution and the resulting coefficient matrix possibly being highly ill-conditioned.…”

Section: Introductionmentioning

confidence: 99%

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A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

Zhang

2022

Numerical Meth Engineering

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High‐order finite element method (FEM) has recently achieved significant success in solving acoustic problems and has proved to be accurate, robust, and capable of reducing the pollution effect. Inspired by the high‐order FEM, this study presents a novel high‐order collocation indirect BEM for solving three‐dimensional high‐frequency exterior acoustic problems. Due to the difficulty of evaluating hypersingular integrals on curved surface elements with complex density functions, the high‐order BEM scheme for acoustic problems has long been a challenging task, especially for relatively large‐scale problems. In the developed scheme, the Leis formulation is used to overcome the well‐known nonuniqueness problem in the indirect BEM, and an auxiliary integral equation method is presented and employed to regularize the hypersingular integrals in this formulation. The derived regularized boundary integral formulation is mathematically simple and amenable to the elements of arbitrary shape and arbitrary variable interpolation order, and leads to a simple, efficient, and robust algorithm for the calculation of all integrals. Several benchmark examples are investigated to verify the performance of the proposed method. Results demonstrate that the present method is very effective in stimulating the far‐field solution with large wavenumber.

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Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

Zhang

2022

Numerical Meth Engineering

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“…When it comes to large‐scale aeroacoustic problems, the computations with fast BEM are still in its infancy and need to be investigated 23 . Wolf developed a fast multipole boundary element method (FMBEM) in a uniform flow 24 in which Lorentz transformation is used to reduce the convected Helmholtz equation to the standard Helmholtz equation without flow and rigid surface boundary condition is specified in this work.…”

Section: Introductionmentioning

confidence: 99%

A fast multipole boundary element method for three‐dimensional acoustic problems in a subsonic uniform flow

Liu

Jiang

et al. 2020

Numerical Methods in Fluids

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A fast multipole boundary element method (FMBEM) in a subsonic uniform flow is presented. It is based on the boundary integral equation (BIE) in a subsonic uniform flow. The convected Green's function complicates its multipole expansion as well as the implementation of the computer code. Although the Lorentz transformation allows the Helmholtz equation in the uniform flow to be reduced to the standard Helmholtz equation, the deformation of the domain complicates the boundary conditions and may cause the elements' distortion. In this work, the analytical evaluations of singular integrals are achieved. Then a nonsingular BIE in a subsonic uniform flow is obtained and is incorporated in building FMBEM with the plane wave multipole expansion of Green's function directly. Details on the implementation of the algorithm are described. Numerical examples including a pulsating sphere radiation problem, a multibody scattering problem and an aircraft model are performed to validate the accuracy and efficiency of the proposed method. Results show that FMBEM solutions are in good agreement with analytical solutions. The difference between the analytical moments and numerical moments is also investigated carefully in the implementation of the fast multipole method. Dramatical improvements on solution efficiency are observed by comparing the developed algorithm with the CBEM.

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Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

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A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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On the BEM for acoustic wave problems

Cited by 59 publications

References 106 publications

A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

A fast multipole boundary element method for three‐dimensional acoustic problems in a subsonic uniform flow

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

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