scholarly journals A Fast-Multipole Unified Technique For The Analysis Of Potential Problems With The Boundary Element Methods

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Ney Augusto Dumont ◽  
Helvio De Farias Costa Peixoto
Keyword(s):  
Boundary Element ◽  
Boundary Element Methods ◽  
Fast Multipole ◽  
Potential Problems

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.

Blake, bubbles and boundary element methods

2019 ◽  
Vol 85 (2) ◽  
pp. 190-213
Author(s):  
Siew-Wan Ohl ◽  
Md Haiqal Haqim Bin Md. Rahim ◽  
Evert Klaseboer ◽  
Boo Cheong Khoo
Keyword(s):  
Boundary Element ◽  
Wave Equations ◽  
Bubble Dynamics ◽  
Acoustic Cavitation ◽  
Boundary Element Methods ◽  
Scientific Career ◽  
Considerable Part ◽  
Numerical Studies ◽  
Potential Problems ◽  
Rigid Surfaces

Abstract Professor John Blake spent a considerable part of his scientific career on studying bubble dynamics and acoustic cavitation. As Blake was a mathematician, we will be focusing on the theoretical and numerical studies (and much less on experimental results). Rather than repeating what is essentially already known, we will try to present the results from a different perspective as much as possible. This review will also be of interest for readers who wish to know more about the boundary element method in general, which is a method often used by Blake and his colleagues to simulate bubbles. We will, however, not limit the discussion to bubble dynamics but try to give a broad discussion on recent advances and improvements to this method, especially for potential problems (Laplace) and wave equations (Helmholtz). Based on examples from Blake’s work, we will guide the reader and show some of the mysteries of bubble dynamics, such as why jets form in collapsing bubbles near rigid surfaces. Where appropriate, we will illustrate the concepts with examples drawn from numerical simulations and experiments.

Sign in / Sign up

Export Citation Format

Share Document