scholarly journals A new diagonal form fast multipole boundary element method for solving acoustic Helmholtz equation

2012 ◽  
Vol 61 (6) ◽  
pp. 064301
Author(s):  
Li Shan-De ◽  
Huang Qi-Bai ◽  
Li Tian-Yun
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Element Method

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.

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.

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