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

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.

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.

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 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.

scholarly journals VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method

2016 ◽  
Author(s):  
Chunxiao Yu ◽  
Cuihuan Ren ◽  
Xueting Bai
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Linear Equations ◽  
Iteration Algorithm ◽  
Fast Multipole ◽  
Minimal Residual Method ◽  
Generalized Inverse Matrix ◽  
Selection Of ◽  
Element Method

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector rm+1 on rm is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.

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