A 3D BOUNDARY ELEMENT METHOD FOR DETERMINATION OF ACOUSTIC EIGENFREQUENCIES CONSIDERING ADMITTANCE BOUNDARY CONDITIONS

1993 ◽  
Vol 01 (04) ◽  
pp. 455-468 ◽  
Author(s):  
Z. S. CHEN ◽  
G. HOFSTETTER ◽  
H. A. MANG
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Numerical Results ◽  
Simple Problem ◽  
Element Method

A 3D boundary element method for the determination of the acoustic eigenfrequencies of car compartments, characterized by a unified treatment of Robin, Dirichlet, and Neumann boundary conditions, is presented. The drawback of frequency-dependent matrices of the eigenvalue problem is overcome by means of the Particular Integral Method. Thus, the standard numerical algorithms for the extraction of eigenvalues can be applied. The numerical study contains both a comparison of numerical results with analytical solutions of a simple problem with different types of boundary conditions and a comparison of numerical results of a large-scale problem with respective numerical results, computed on the basis of the finite element method. In addition, for the latter example, different numerical algorithms for the eigenvalue extraction are examined.

A TECHNIQUE FOR PLANE-SYMMETRIC SOUND FIELD ANALYSIS IN THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD

2005 ◽  
Vol 13 (01) ◽  
pp. 71-85 ◽  
Author(s):  
Y. YASUDA ◽  
T. SAKUMA
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Sound Field ◽  
Field Analysis ◽  
Fast Multipole ◽  
Plane Symmetric ◽  
Sound Fields ◽  
Element Method

The fast multipole boundary element method (FMBEM) is an advanced BEM, with which both the operation count and the memory requirements are O(Na log b N) for large-scale problems, where N is the degree of freedom (DOF), a ≥ 1 and b ≥ 0. In this paper, an efficient technique for analyses of plane-symmetric sound fields in the acoustic FMBEM is proposed. Half-space sound fields where an infinite rigid plane exists are typical cases of these fields. When one plane of symmetry is assumed, the number of elements and cells required for the FMBEM with this technique are half of those for the FMBEM used in a naive manner. In consequence, this technique reduces both the computational complexity and the memory requirements for the FMBEM almost by half. The technique is validated with respect to accuracy and efficiency through numerical study.

AN EFFECTIVE SETTING OF HIERARCHICAL CELL STRUCTURE FOR THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD

2005 ◽  
Vol 13 (01) ◽  
pp. 47-70 ◽  
Author(s):  
Y. YASUDA ◽  
T. SAKUMA
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Cell Structure ◽  
Sound Field ◽  
Field Analysis ◽  
Fast Multipole ◽  
Simple Method ◽  
Element Method

The fast multipole boundary element method (FMBEM) is an advanced BEM that leads to drastic reduction of processing time and memory requirements in a large-scale steady-state sound field analysis. In the FMBEM, hierarchical cell structure is employed to apply multipole expansion in multiple levels, and the setting of the hierarchical cell structure considerably affects the computational efficiency of the FMBEM. This paper deals with effective settings of hierarchical cell structure for taking full advantage of the FMBEM. A numerical study with objects of different shapes with the same DOF shows that both the computational complexity and the memory requirements with the FMBEM were greater for 1D-shaped objects than for 2D- or 3D-shaped ones, without a special setting of hierarchical cell structure for each problem. An effective setting for 1D-shaped objects is derived through theoretical and numerical studies, where special considerations are given to the arrangement of the cell structure and the treatment of translation coefficients between cells. This setting allows for efficient calculations not dependent on the shape of an analyzed object. A simple method to arrange hierarchical cell structure is proposed, which realizes the derived setting for arbitrarily-shaped problems.

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.

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

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.

scholarly journals Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

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