scholarly journals A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

2020 ◽  
Vol 121 (21) ◽  
pp. 4734-4767
Author(s):  
Damien Mavaleix‐Marchessoux ◽  
Marc Bonnet ◽  
Stéphanie Chaillat ◽  
Bruno Leblé
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Frequency ◽  
Large Scale ◽  
Three Dimensional ◽  
Transient Wave ◽  
Wave Problems ◽  
Element Method

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.

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 for Three-Dimensional Half-Space Acoustic Wave Problems Over an Impedance Plane

2015 ◽  
Vol 12 (01) ◽  
pp. 1350090 ◽  
Author(s):  
Haijun Wu ◽  
Yijun Liu ◽  
Weikang Jiang ◽  
Wenbo Lu
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Three Dimensional ◽  
The Real ◽  
Impedance Plane ◽  
Real Domain ◽  
Wave Problems ◽  
Element Method

A high-frequency fast multipole boundary element method (FMBEM) based on the Burton–Miller formulation is proposed for three-dimensional acoustic wave problems over an infinite plane with impedance boundary conditions. The Green's function for the sound propagation over an impedance plane is employed explicitly in the boundary integral equation (BIE). To deal with the integral appearing in the half-space Green's function, the downward pass in the FMBEM is divided into two parts to compute contributions from the real domain to the real and image domains, respectively. A piecewise analytical method is proposed to compute the moment-to-local (M2L) translator from the real domain to the image domain accurately. An algorithm based on the multi-level tree structure is designed to compute the M2L translators efficiently. Correspondingly, the direct coefficient can also be computed efficiently by taking advantage of the algorithm of the efficient M2L. A flexible generalized minimal residual (fGMRES) is applied to accelerating the solution when the convergence is very slow. Numerical examples are presented to demonstrate the accuracy and efficiency of the developed FMBEM. Good solutions and high acceleration ratios compared with the conventional boundary element method clearly show the potential of the FMBEM for large-scale 3D acoustic wave problems over an infinite impedance plane which are of practical significance.

Fast Multipole Boundary Element Method for 3-D Full- and Half-Space Acoustic Wave Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Large Scale ◽  
Fast Multipole ◽  
Wave Problems ◽  
Acoustic Bem ◽  
Element Method

In this paper, the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 3-D full- and half-space domains will be discussed. First, the fast multipole BEM formulations will be presented and then improvements to the formulations and algorithms will be discussed. Examples with large-scale acoustic BEM models, with the DOFs above 2 millions and solved on desktop PCs, will be presented to demonstrate the potential of the fast multipole BEM for modeling large-scale structural acoustic problems.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

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