A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering

1997 ◽  
Vol 05 (02) ◽  
pp. 219-241 ◽  
Author(s):  
Z. S. Chen ◽  
G. Hofstetter ◽  
H. A. Mang
Keyword(s):  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Integral Equations ◽  
Acoustic Radiation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Galerkin Formulation ◽  
Thin Walled ◽  
Element Method

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

scholarly journals Numerical study of single bubble mobility in triangular and deltoid microchannels using the boundary element method

2021 ◽  
Vol 2057 (1) ◽  
pp. 012042
Author(s):  
A Z Bulatova ◽  
O A Solnyshkina ◽  
N B Fatkullina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Complex Geometry ◽  
Numerical Study ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Variable Pressure ◽  
Bubbly Liquid ◽  
Element Method

Abstract The study of bubbly liquid dynamics in microchannels of unconventional shapes is of great importance for different fields of science and industry. This work investigates the dynamics of the incompressible single bubbles in the slow periodic flow of viscous liquid in a triangular channel with a variable pressure gradient. The numerical approach used in this research is based on the boundary element method (BEM). This method is widely used for solving three-dimensional problems and problems in areas with complex geometry. The influence of the bubble’s initial position relative to the channel centerline on the bubble deformation, the relative velocity of the bubble, and its center of mass displacement in the channel are considered.

A FORMULATION OF THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD (FMBEM) FOR ACOUSTIC RADIATION AND SCATTERING FROM THREE-DIMENSIONAL STRUCTURES

2008 ◽  
Vol 16 (02) ◽  
pp. 303-320 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE ◽  
W. KREUZER
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Acoustic Radiation ◽  
Three Dimensional ◽  
Efficient Computation ◽  
Fast Multipole ◽  
Head Related Transfer Function ◽  
And Storage ◽  
Element Method

Compared to the traditional boundary element method (BEM), the single level fast multipole boundary element method (SLFMBEM) or the multilevel fast multipole boundary element method (MLFMBEM) reduces the computational complexity of a job from O(n2) to O(n3/2) or O(n log 2n), respectively with n being the number of unknowns; this means a dramatical reduction in terms of CPU-time and storage requirement. Large scale problems, unsolvable with the traditional BEM, can be solved by using the FMBEM. In this paper, the traditional BEM, SLFMBEM, and MLFMBEM are formulated within the framework of the Burton–Miller Collocation BEM for acoustic radiation and scattering from 3D structures. Attention is especially paid to the practical aspects of the method in order to get a reliable and efficient computation code. The performance of the method is tested with practical examples, including one for computing the head-related transfer function (HRTF) between 1000 and 18 000 Hz.

scholarly journals FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR THREE DIMENSIONAL ELECTROMAGNETIC SCATTERING PROBLEM

2012 ◽  
Vol 01 (04) ◽  
pp. 1250038 ◽  
Author(s):  
S. B. WANG ◽  
H. H. ZHENG ◽  
J. J. XIAO ◽  
Z. F. LIN ◽  
C. T. CHAN
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Triangular Grid ◽  
Fast Multipole ◽  
Electromagnetic Plane Wave ◽  
Element Method

We developed a fast numerical algorithm for solving the three-dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nyström's quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.

scholarly journals Thermoelasticity if isotropic solids containing non-deformable thread-like inclusions

2019 ◽  
pp. 33-41
Author(s):  
Jaroslav Pasternak ◽  
Heorhiy Sulym ◽  
Nataliia Ilchuk
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Integral Equations ◽  
Numerical Example ◽  
Thermally Conducting ◽  
Isotropic Solids ◽  
Element Method

The paper derives integral equations of heat conduction and thermoelasticity of isotropic solids with non-deformable perfectly thermally conducting thread-like inclusions. It is observed that, in spite of the order of singularity, the integral equations obtained are hypersingular due to the symmetry of the kernels. Non-integral terms of these equations are derived. A boundary element method scheme for numerical solution of formulated problems is proposed. A numerical example is provided.

A FORMULATION OF THE BOUNDARY ELEMENT METHOD FOR ACOUSTIC RADIATION AND SCATTERING FROM TWO-DIMENSIONAL STRUCTURES

2007 ◽  
Vol 15 (03) ◽  
pp. 333-352 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Ground Surface ◽  
Green Functions ◽  
Two Dimensional ◽  
Element Method

A code for the boundary element method (BEM) for two-dimensional acoustic radiation and scattering problems is developed. To overcome the singularity problem of the integral equations at characteristic frequencies, the Burton–Miller method is employed in the formulation. The integral equations are then discretized by using the two-nodal constant elements and a collocation procedure. The hyper and weakly singular integrals in each element containing the collocation points are computed analytically and numerically respectively (stark singularity does not appear). In outdoor acoustic, the ground surface can be seen occasionally as an infinite surface with a given constant impedance. In this case the ground surface can either be discretized by using finite and infinite boundary elements or simulated by using the Green functions for impedance half space. The method to compute such Green functions presented in Ref. 1, is improved and used in the code. A formulation of the infinite boundary element is proposed. The two BEM approaches for the impedance half space problems are tested by means of examples and the agreement is found to be good.

Application of the Boundary Element Method and Modal Analysis to Tire Acoustics Problems

1993 ◽  
Vol 21 (2) ◽  
pp. 66-90 ◽  
Author(s):  
Y. Nakajima ◽  
Y. Inoue ◽  
H. Ogawa
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Traffic Noise ◽  
Noise Prediction ◽  
Prediction System ◽  
Tire Noise ◽  
Acoustic Contribution ◽  
Element Method

Abstract Road traffic noise needs to be reduced, because traffic volume is increasing every year. The noise generated from a tire is becoming one of the dominant sources in the total traffic noise because the engine noise is constantly being reduced by the vehicle manufacturers. Although the acoustic intensity measurement technology has been enhanced by the recent developments in digital measurement techniques, repetitive measurements are necessary to find effective ways for noise control. Hence, a simulation method to predict generated noise is required to replace the time-consuming experiments. The boundary element method (BEM) is applied to predict the acoustic radiation caused by the vibration of a tire sidewall and a tire noise prediction system is developed. The BEM requires the geometry and the modal characteristics of a tire which are provided by an experiment or the finite element method (FEM). Since the finite element procedure is applied to the prediction of modal characteristics in a tire noise prediction system, the acoustic pressure can be predicted without any measurements. Furthermore, the acoustic contribution analysis obtained from the post-processing of the predicted results is very helpful to know where and how the design change affects the acoustic radiation. The predictability of this system is verified by measurements and the acoustic contribution analysis is applied to tire noise control.

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