120 A Study on Numerical Analysis of High Frequency Sound Field in a Cabin of a Car Using 3-Dimensional Fast Multipole Boundary 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.

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The improvement of computational efficiency of three-dimensional sound field analysis by boundary element method using two-level fast multipole method

Electronics and Communications in Japan (Part III Fundamental Electronic Science) ◽

10.1002/ecjc.1110 ◽

2002 ◽

Vol 85 (8) ◽

pp. 30-37

Author(s):

Yohzoh Okumura

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Computational Efficiency ◽

Fast Multipole Method ◽

Three Dimensional ◽

Sound Field ◽

Field Analysis ◽

Fast Multipole ◽

Multipole Method ◽

Element Method

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

Journal of Computational Acoustics ◽

10.1142/s0218396x05002529 ◽

2005 ◽

Vol 13 (01) ◽

pp. 47-70 ◽

Cited By ~ 15

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.

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A modified dual-level fast multipole boundary element method based on the Burton–Miller formulation for large-scale three-dimensional sound field analysis

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2018.05.016 ◽

2018 ◽

Vol 340 ◽

pp. 121-146 ◽

Cited By ~ 15

Author(s):

Junpu Li ◽

Wen Chen ◽

Qinghua Qin

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Large Scale ◽

Three Dimensional ◽

Sound Field ◽

Field Analysis ◽

Fast Multipole ◽

Element Method

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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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