no. 11-12
Numerical Analysis
FE heterogeneous multiscale method for long-time wave propagation
[Méthode dʼéléments finis multi-échelles pour lʼéquation des ondes dans des milieux hétérogènes sur des temps longs]

Présenté par : Olivier Pironneau

Abdulle, Assyr1 ; Grote, Marcus J.2 ; Stohrer, Christian2
1 ANMC, Section de mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
2 Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 495-499.

Dans cet article, nous proposons une nouvelle méthode dʼéléments finis multi-échelles pour la solution de lʼéquation des ondes dans des milieux hétérogènes sur des temps longs. Cette méthode numérique est capable dʼapprocher le comportement effectif de la solution sur des temps longs, avec un coût identique à celui dʼune méthode dʼhomogénéisation numérique standard, qui ne peut capturer le comportement effectif de la solution que sur des temps courts.

A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our FE-HMM captures long-time dispersive effects of the true solution at a cost similar to that of a standard numerical homogenization scheme which, however, only captures the short-time macroscale behavior of the wave field.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.06.002
Abdulle, Assyr 1 ; Grote, Marcus J. 2 ; Stohrer, Christian 2

1 ANMC, Section de mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
2 Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland 
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Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian. FE heterogeneous multiscale method for long-time wave propagation. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 495-499. doi : 10.1016/j.crma.2013.06.002. http://www.numdam.org/articles/10.1016/j.crma.2013.06.002/

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