A fast multipole boundary element method based on the improved Burton–Miller formulation for three-dimensional acoustic problems

2011 ◽  
Vol 35 (5) ◽  
pp. 719-728 ◽  
Author(s):  
Shande Li ◽  
Qibai Huang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Fast Multipole ◽  
Element Method

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

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.

A Fast Multipole Boundary Element Method Based on Legendre Series for Three-Dimensional Potential Problems

2012 ◽  
Vol 468-471 ◽  
pp. 426-429
Author(s):  
Chun Xiao Yu ◽  
Hai Yuan Yu ◽  
Yi Ming Chen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Multipole Expansion ◽  
Fundamental Solutions ◽  
Fast Multipole ◽  
Legendre Series ◽  
Truncation Errors ◽  
Potential Problems ◽  
Element Method

Vectorization expressions of a Fast Multipole Boundary Element Method (FM-BEM) based on Legendre series are presented for three-dimensional (3-D) potential problems. The formulas are applied to the expression of fundamental solutions for the Boundary Element Method(BEM). Truncation errors of the multipole expansion and local expansion are deduced and analyzed. It shows that the errors can be controlled by truncation terms.

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