A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain

Stéphanie Chaillat; Marc Bonnet; Jean-François Semblat

doi:10.1016/j.crme.2007.07.001

A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain

Presented by: Jean-Baptiste Leblond

Stéphanie Chaillat ^1,²; Marc Bonnet ¹ ; Jean-François Semblat ²

¹ LMS, CNRS UMR 7649, École polytechnique, 91128 Palaiseau cedex, France
² LCPC, 58, boulevard Lefebvre, 75732 Paris cedex 15, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 714-719.

Abstract
Résumé

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 $N \log_{2} N$ per GMRES iteration. The present Note address the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Its efficiency and accuracy are demonstrated on numerical examples involving up to $N = O (10^{6})$ nodal unknowns.

La résolution des équations de l'élastodynamique par la méthode des éléments de frontière (BEM) conduit à un système linéaire plein. Des travaux récents sur les équations de Helmholtz et Maxwell ont établi la capacité de la méthode multipôle rapide (FM) à réduire la complexité de la BEM à $N \log_{2} N$ par itération d'un solveur de type GMRES. Cette Note présente l'extension de l'approche FM-BEM à l'élastodynamique 3D dans le domaine fréquentiel. La précision et l'efficacité de la méthode sont illustrées sur des exemples numériques mobilisant jusqu'à $N = O (10^{6})$ inconnues nodales.

Received: 2007-01-10
Accepted: 2007-07-10
Published online: 2007-09-19

DOI: 10.1016/j.crme.2007.07.001

Keywords: Computational solid mechanics, Boundary element method, Fast multipole method, 3D elastodynamics
Mot clés : Mécanique des solides numérique, Éléments de frontière, Méthode multipôle rapide, Élastodynamique 3D

Author's affiliations:

Stéphanie Chaillat ^{1, 2}; Marc Bonnet ¹; Jean-François Semblat ²

¹ LMS, CNRS UMR 7649, École polytechnique, 91128 Palaiseau cedex, France
² LCPC, 58, boulevard Lefebvre, 75732 Paris cedex 15, France

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     author = {St\'ephanie Chaillat and Marc Bonnet and Jean-Fran\c{c}ois Semblat},
     title = {A {Fast} {Multipole} {Method} formulation for {3D} elastodynamics in the frequency domain},
     journal = {Comptes Rendus. M\'ecanique},
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Stéphanie Chaillat; Marc Bonnet; Jean-François Semblat. A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain. Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 714-719. doi : 10.1016/j.crme.2007.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.07.001/

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