Fast multipole accelerated boundary element method for the Helmholtz equation in acoustic scattering problems

2011 ◽  
Vol 54 (8) ◽  
pp. 1405-1410 ◽  
Author(s):  
ShanDe Li ◽  
GuiBing Gao ◽  
QiBai Huang ◽  
WeiQi Liu ◽  
Jun Chen
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Acoustic Scattering ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Element Method ◽  
Acoustic Scattering Problems

Subdivision Surfaces — Boundary Element Accelerated by Fast Multipole for the Structural Acoustic Problem

2020 ◽  
Vol 28 (02) ◽  
pp. 2050011
Author(s):  
Leilei Chen ◽  
Chuang Lu ◽  
Wenchang Zhao ◽  
Haibo Chen ◽  
Changjun Zheng
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Computer Aided Design ◽  
Geometric Model ◽  
Subdivision Surfaces ◽  
Surface Boundary ◽  
Subdivision Scheme ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Element Method

A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis.

Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems

2020 ◽  
Vol 28 (4) ◽  
pp. 223-245
Author(s):  
Gabriel N. Gatica ◽  
Salim Meddahi
Keyword(s):  
Boundary Element ◽  
Acoustic Scattering ◽  
Rates Of Convergence ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Combined Use ◽  
Virtual Element ◽  
2D And 3D ◽  
Element Method ◽  
Acoustic Scattering Problems

AbstractThis paper extends the applicability of the combined use of the virtual element method (VEM) and the boundary element method (BEM), recently introduced to solve the coupling of linear elliptic equations in divergence form with the Laplace equation, to the case of acoustic scattering problems in 2D and 3D. The well-posedness of the continuous and discrete formulations are established, and then Cea-type estimates and consequent rates of convergence are derived.

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