Fast Multipole Boundary Element Method for 3-Dimension Acoustic Radiation Problem

2011 ◽  
Vol 130-134 ◽  
pp. 80-85
Author(s):  
Bing Rong Zhang ◽  
Jian Chen ◽  
Li Tao Chen ◽  
Wu Zhang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Acoustic Radiation ◽  
Cell Structure ◽  
Level Structure ◽  
Iterative Solvers ◽  
Influence Coefficient ◽  
Fast Multipole ◽  
Element Method

In order to reduce computational complexity and memory requirements using conventional boundary element method (CBEM) for large scale acoustical analysis, a fast solving algorithm called the Fast Multipole BEM (FMBEM) based on the fast multipole algorithm and GMRES iterative solver is developed without composing the dense influence coefficient matrices. The multipole level structure is introduced to accelerate the solution of large-scale acoustical problems, by employing a concept of cells clustering boundary elements and hierarchical cell structure. To further improve the efficiency of the FMBEM with iterative solvers, a block diagonal matrix method is used in the system of equations as the left pre-conditioner. Numerical examples are presented to further demonstrate the efficiency, accuracy and potentials of the fast multipole BEM for solving large-scale acoustical problems.

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.

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.

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.

The Mixed Fast Multipole Boundary Element Method for Solving Strip Cold Rolling Process

2010 ◽  
Vol 20-23 ◽  
pp. 76-81 ◽  
Author(s):  
Hai Lian Gui ◽  
Qing Xue Huang
Keyword(s):  
Variational Inequality ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Mixed Boundary ◽  
Contact Problems ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Mixed Variational Inequality ◽  
Element Method

Based on fast multipole boundary element method (FM-BEM) and mixed variational inequality, a new numerical method named mixed fast multipole boundary element method (MFM-BEM) was presented in this paper for solving three-dimensional elastic-plastic contact problems. Mixed boundary integral equation (MBIE) was the foundation of MFM-BEM and obtained by mixed variational inequality. In order to adapt the requirement of fast multipole method (FMM), Taylor series expansion was used in discrete MBIE. In MFM-BEM the calculation time was significant decreased, the calculation accuracy and continuity was also improved. These merits of MFM-BEM were demonstrated in numerical examples. MFM-BEM has broad application prospects and will take an important role in solving large-scale engineering problems.

Application Incompatible Element in Mixed Fast Multipole Boundary Element Method

2010 ◽  
Vol 439-440 ◽  
pp. 80-85
Author(s):  
Hai Lian Gui ◽  
Qing Xue Huang ◽  
Ya Qin Tian ◽  
Zhi Bing Chu
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Fast Multipole ◽  
Mixed Variational Inequality ◽  
Calculation Time ◽  
Incompatible Elements ◽  
Improve Calculation ◽  
Compatible Elements ◽  
Element Method

Based on fast multipole boundary element method (FM-BEM) and mixed variational inequality, a new method named mixed fast multipole boundary element method (MFM-BEM) was presented in this paper. In order to improve calculation time and accuracy, incompatible elements as interpolation functions were used in the algorithm. Elements were optimized by mixed incompatible elements and compatible elements. On the one hand, the difficult to satisfy precise coordinate was avoided which caused by compatible elements; on the other hand, the merits of MFM-BEM were retained. Through analysis of example, it was conclusion that calculation time and accuracy were improved by MFM-BEM, calculation continuity was also better than traditional FM-BEM. With increasing of degree of freedom, calculation time of MFM-BEM grew slower than the time of traditional FM-BEM. So MFM-BEM provided a theoretical basis for solving large-scale engineering problems.

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.

A New Fast Multipole Boundary Element Method for Solving 3-D Elastic Problem

2013 ◽  
Vol 813 ◽  
pp. 387-390
Author(s):  
Hai Lian Gui ◽  
Qiang Li ◽  
Yu Gui Li ◽  
Xia Yang ◽  
Qing Xue Huang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Taylor Series ◽  
Large Scale ◽  
Taylor Series Expansion ◽  
Elastic Problem ◽  
Fast Multipole ◽  
Influence Coefficients ◽  
Boundary Cell ◽  
Element Method

In this paper, a new fast multipole boundary element method is presented. By using Taylor series expansion and a new mapping in boundary cell, the efficiency of calculation about influence coefficients has been improved. Compare with the old fast multipole boundary element method, this new method is easier to be suitable for the large-scale numerical calculus request.

FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR LOW-FREQUENCY ACOUSTIC PROBLEMS BASED ON A VARIETY OF FORMULATIONS

2010 ◽  
Vol 18 (04) ◽  
pp. 363-395 ◽  
Author(s):  
YOSUKE YASUDA ◽  
TAKUYA OSHIMA ◽  
TETSUYA SAKUMA ◽  
ARIEF GUNAWAN ◽  
TAKAYUKI MASUMOTO
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cell Structure ◽  
Low Frequency ◽  
Multipole Expansion ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Computational Accuracy ◽  
Low Frequencies ◽  
Element Method

The fast multipole boundary element method (FMBEM), which is an efficient BEM that uses the fast multipole method (FMM), is known to suffer from instability at low frequencies when the well-known high-frequency diagonal form is employed. In the present paper, various formulations for a low-frequency FMBEM (LF-FMBEM), which is based on the original multipole expansion theory, are discussed; the LF-FMBEM can be used to prevent the low-frequency instability. Concrete computational procedures for singular, hypersingular, Burton-Miller, indirect (dual BEM), and mixed formulations are described in detail. The computational accuracy and efficiency of the LF-FMBEM are validated by performing numerical experiments and carrying out a formal estimation of the efficiency. Moreover, practically appropriate settings for numerical items such as truncation numbers for multipole/local expansion coefficients and the lowest level of the hierarchical cell structure used in the FMM are investigated; the differences in the efficiency of the LF-FMBEM when different types of formulations are used are also discussed.

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