Application of Fast Multipole Boundary Element Method to Multiple Scattering Analysis of Acoustic and Elastic Waves

2007 ◽  
Author(s):  
T. Saitoh ◽  
S. Hirose ◽  
T. Fukui
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Fast Multipole ◽  
Element Method

scholarly journals Multiple Scattering Approximation of Anti-plane Elastic Waves in Infinite and Half-Space Domains with Distributed Inclusions

2007 ◽  
Vol 4 (1) ◽  
Author(s):  
Kwannate Tharmmapornphilas ◽  
Sohichi Hirose
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Multiple Scattering ◽  
Half Space ◽  
Elastic Waves ◽  
Scattered Wave ◽  
Computational Time ◽  
Calculation Point ◽  
Scattering Of Elastic Waves ◽  
Element Method

This paper presents an approximation for multiple scattering of elastic waves in the frequency domain by cylindrical inclusions. The problem is reduced to a 2D model by assuming circular inclusions. These inclusions are distributed at randomly selected points in 2D isotropic solids. Infinite and half-space matrices are considered. The inclusions are subjected to an anti-plane (SH) incident wave. The proposed approximation is based on the assumption that the multiple scattering displacement is the summation of the effects of all the possible wave propagation paths. If a wave hits one inclusion, the wave is scattered and part of it scatters to the calculation point. The wave also scatters to the other inclusions and thus repeating the process. This process is repeated a lot of times but the scattered wave becomes smaller as the path length increases and thus becomes negligible up to a certain order. Each of these scattered waves is approximated using the displacements calculated using the boundary element method with farfield approximation for a single scatterer. Using the proposed approximation, the computational time and the memory requirement are considerably reduced as compared to the conventional boundary element method. Numerical results for two aligned inclusions, thirty randomly selected and hundred randomly placed inclusions in both infinite and half-space matrices are shown to verify the accuracy of the proposed approximation.

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 A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

2014 ◽  
Vol 1 (4) ◽  
pp. CM0039-CM0039 ◽  
Author(s):  
Hiroshi ISAKARI ◽  
Kohei KURIYAMA ◽  
Shinya HARADA ◽  
Takayuki YAMADA ◽  
Toru TAKAHASHI ◽  
...  
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Topology Optimisation ◽  
Fast Multipole ◽  
Element Method

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.

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