On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics

2005 ◽  
Vol 29 (7) ◽  
pp. 673-688 ◽  
Author(s):  
Haitao Wang ◽  
Zhenhan Yao ◽  
Pengbo Wang
Keyword(s):  
Boundary Element ◽  
Boundary Element Methods ◽  
Fast Multipole

scholarly journals A fast multipole accelerated BEM for 3-D elastic wave computation

2008 ◽  
pp. 701-712
Author(s):  
Stéphanie Chaillat ◽  
Marc Bonnet ◽  
Jean- François Semblat
Keyword(s):  
Elastic Wave ◽  
Frequency Domain ◽  
Boundary Element ◽  
Present Article ◽  
Maxwell Equations ◽  
Boundary Element Methods ◽  
Matrix Equations ◽  
Fast Multipole ◽  
Numerical Examples ◽  
Gmres Iteration

The solution of the elastodynamic equations using boundary element methods (BEMs) gives rise to fully-populated matrix equations. Earlier investigations on the Helmholtz and Maxwell equations have established that the Fast Multipole (FM) method reduces the complexity of a BEM solution to N log2 N per GMRES iteration. The present article addresses the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Efficiency and accuracy are demonstrated on numerical examples involving up to N = O(106) boundary nodal unknowns.

scholarly journals Implementation of Isogeometric Fast Multipole Boundary Element Methods for 2D Half-Space Acoustic Scattering Problems with Absorbing Boundary Condition

2019 ◽  
Vol 27 (02) ◽  
pp. 1850024 ◽  
Author(s):  
Leilei Chen ◽  
Steffen Marburg ◽  
Wenchang Zhao ◽  
Cheng Liu ◽  
Haibo Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Half Space ◽  
Boundary Element Methods ◽  
Absorbing Boundary Condition ◽  
Fast Multipole ◽  
Absorbing Boundary ◽  
Computer Aided ◽  
Element Method

Isogeometric Analysis (IGA), which tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD), has been widely proposed in recent research. According to the concept of IGA, this work develops a boundary element method (BEM) using non-Uniform Rational B-Splines (NURBS) as basis functions for the 2D half-space acoustic problems with absorbing boundary condition. Fast multipole method (FMM) is applied to accelerate the solution of an isogeometric BEM (IGA-BEM). Several examples are tested and it is shown that this advancement on isogeometric fast multipole boundary element method improves the accuracy of simulations.

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