Fast Calculation of Far-Field Sound Directivity Based on Fast Multipole Boundary Element Method

A fast method for calculating sound radiation/reflection directivities at high resolution in the infinite far field is proposed with the use of the fast multipole boundary element method (FMBEM). This method calculates directivities using direction-dependent coefficients called outgoing coefficients, which are obtained in the calculation process of the matrix-vector products in the FMBEM. Since the outgoing coefficients are generally calculated for a large number of directions high-resolution directivities can be easily obtained with extremely small computational cost and minor modifications in the FMBEM program codes. It is confirmed via comparison with the numerical results using the conventional method that the proposed method can calculate directivities at infinity. Numerical results also show that the computational time for the proposed method is significantly shorter than that for the conventional method with no addition of the required memory.

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Numerical Integral Independent of Frequency in the Boundary Element Method for Acoustic Scattering

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.444-445.650 ◽

2013 ◽

Vol 444-445 ◽

pp. 650-654

Author(s):

Zai You Yan ◽

Chuan Zhen Li

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Acoustic Scattering ◽

Normal Derivative ◽

Numerical Results ◽

New Technique ◽

Computational Time ◽

Unknown Variable ◽

Numerical Integral ◽

Element Method

Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.

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Application of the Fast Multipole Boundary Element Method to Analysis of Sound Fields in Absorbing Materials

Volume 13: New Developments in Simulation Methods and Software for Engineering Applications; Safety Engineering, Risk Analysis and Reliability Methods; Transportation Systems ◽

10.1115/imece2009-10698 ◽

2009 ◽

Author(s):

Xiaobing Cui ◽

Zhenlin Ji

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Large Scale ◽

Computational Time ◽

Fast Multipole ◽

Computational Accuracy ◽

Decomposition Approach ◽

Sound Fields ◽

Absorbing Material ◽

Element Method

As an advanced boundary element method (BEM) employing the fast multipole algorithm, the fast multipole boundary element method (FMBEM) has been developed to realize fast computation and drastic memory saving for the large-scale problems. In the present study, The FMBEM is applied to analyze the interior sound fields that partially-filled with sound-absorbing material. The basic principle of FMBEM is introduced briefly, and the domain decomposition approach for FMBEM is investigated. The numerical errors in multipole expansions are analyzed in order to obtain the sufficient accuracy for the FMBEM computation of sound fields in sound-absorbing material. The sound pressures in a duct partially-filled with sound-absorbing material are calculated by using the present FMBEM and the conventional BEM, and then the computational accuracy and efficiency of FMBEM are discussed by comparing the results from the two methods. The numerical results showed that the FMBEM is capable to deal with the sound fields problems in sound-absorbing material, and can save computational time for the acoustic problems with large number of nodes.

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Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

Water Science & Technology ◽

10.2166/wst.1991.0451 ◽

1991 ◽

Vol 23 (1-3) ◽

pp. 517-524

Author(s):

M. Kanoh ◽

T. Kuroki ◽

K. Fujino ◽

T. Ueda

Keyword(s):

Boundary Element Method ◽

Finite Difference ◽

Finite Difference Method ◽

Boundary Element ◽

Difference Method ◽

Groundwater Pollution ◽

Small Region ◽

Boundary Element Methods ◽

Computational Time ◽

Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

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Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

Volume 15: Sound, Vibration and Design ◽

10.1115/imece2009-10163 ◽

2009 ◽

Author(s):

Yijun Liu ◽

Milind Bapat

Keyword(s):

Boundary Element Method ◽

Acoustic Wave ◽

Boundary Element ◽

Large Scale ◽

Boundary Integral ◽

Practical Significance ◽

Fast Multipole ◽

Tree Structures ◽

Wave Problems ◽

Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

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Hydrodynamic Interactions in Multiple Body Array: A Simple and Fast Approach Coupling Boundary Element Method and Plane Wave Approximation

Volume 5: Ocean Engineering ◽

10.1115/omae2013-10541 ◽

2013 ◽

Author(s):

Jitendra Singh ◽

Aurélien Babarit

Keyword(s):

Boundary Element Method ◽

Plane Wave ◽

Boundary Element ◽

Hydrodynamic Interaction ◽

Computational Time ◽

Linear Potential ◽

Wave Approximation ◽

Interaction Problem ◽

Plane Wave Approximation ◽

Element Method

The hydrodynamic forces acting on an isolated body could be considerably different than those when it is considered in an array of multiple bodies, due to wave interactions among them. In this context, we present in this paper a numerical approach based on the linear potential flow theory to solve full hydrodynamic interaction problem in a multiple body array. In contrast to the previous approaches that considered all bodies in an array as a single unit, the present approach relies on solving for an isolated body. The interactions among the bodies are then taken into account via plane wave approximation in an iterative manner. The boundary value problem corresponding to a isolated body is solved by the Boundary Element Method (BEM). The approach is useful when the bodies are sufficiently distant from each other, at-least greater than five times the characteristic dimensions of the body. This is a valid assumption for wave energy converter devices array of point absorber type, which is our target application at a later stage. The main advantage of the proposed approach is that the computational time requirement is significantly less than the commonly used direct BEM. The time savings can be realized for even small arrays consisting of four bodies. Another advantage is that the computer memory requirements are also significantly smaller compared to the direct BEM, allowing us to consider large arrays. The numerical results for hydrodynamic interaction problem in two arrays consisting of 25 cylinders and same number of rectangular flaps are presented to validate the proposed approach.

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An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

Journal of Fluids Engineering ◽

10.1115/1.4037690 ◽

2017 ◽

Vol 140 (1) ◽

Author(s):

Sofia Sarraf ◽

Ezequiel López ◽

Laura Battaglia ◽

Gustavo Ríos Rodríguez ◽

Jorge D'Elía

Keyword(s):

Boundary Element Method ◽

Linear System ◽

Boundary Element ◽

Numerical Solutions ◽

Three Dimensional ◽

Boundary Integral ◽

Computational Time ◽

Creeping Flows ◽

Order Of Magnitude ◽

Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

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