Computation of the head-related transfer function via the fast multipole accelerated boundary element method and its spherical harmonic representation

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.

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Fast calculation system specialized for head-related transfer function based on boundary element method

The Journal of the Acoustical Society of America ◽

10.1121/1.2191608 ◽

2006 ◽

Vol 119 (5) ◽

pp. 2589-2598 ◽

Cited By ~ 57

Author(s):

Makoto Otani ◽

Shiro Ise

Keyword(s):

Boundary Element Method ◽

Transfer Function ◽

Boundary Element ◽

Fast Calculation ◽

Head Related Transfer Function ◽

Calculation System ◽

Element Method

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Boundary element method calculation of individual head-related transfer function. II. Impedance effects and comparisons to real measurements

The Journal of the Acoustical Society of America ◽

10.1121/1.1412441 ◽

2001 ◽

Vol 110 (5) ◽

pp. 2449-2455 ◽

Cited By ~ 41

Author(s):

Brian F. G. Katz

Keyword(s):

Boundary Element Method ◽

Transfer Function ◽

Boundary Element ◽

Method Calculation ◽

Head Related Transfer Function ◽

Element Method

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Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

Volume 15: Sound, Vibration and Design ◽

10.1115/imece2009-10163 ◽

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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