Sensitivity of solutions computed through the Asymptotic Numerical Method

Isabelle Charpentier

doi:10.1016/j.crme.2008.09.003

Sensitivity of solutions computed through the Asymptotic Numerical Method

Presented by: Évariste Sanchez-Palencia

Isabelle Charpentier ¹

¹ Laboratoire de physique et mécanique des matériaux, UMR 7554, Île du Saulcy, 57045 Metz cedex 1, France

Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 788-793.

Abstract
Résumé

The Asymptotic Numerical Method (ANM) allows one to compute solution branches of sufficiently smooth non-linear PDE problems using truncated Taylor expansions. The Diamant approach of the ANM has been proposed for hiding definitively the differentiation aspects to the user. In this Note, this significant improvement in terms of genericity is exploited to compute the sensitivity of ANM solutions with respect to modelling parameters. The differentiation in the parameters is discussed at both the equation and code level to highlight the Automatic Differentiation (AD) purposes. A numerical example proves the interest of such techniques for a generic and efficient implementation of sensitivity computations.

La Méthode Asymptotique Numérique (MAN) permet de calculer des branches de solutions de problèmes d'EDP suffisamment réguliers à l'aide de séries de Taylor tronquées. L'approche Diamant de la MAN a été proposée pour cacher définitivement les aspects différentiation à l'utilisateur. Dans cette Note, cette amélioration significative en terme de généricité est exploitée pour calculer la sensibilité des solutions MAN par rapport aux paramètres de modélisation. La différentiation en les paramètres est discutée au niveau des équations et du code pour souligner les aspects Différentiation Automatique (DA). Un exemple numérique prouve l'intérêt de ces techniques pour l'implémentation générique et efficace de calculs de sensibilité.

Received: 2008-03-18
Accepted: 2008-09-01
Published online: 2008-10-01

DOI: 10.1016/j.crme.2008.09.003

Keywords: Continuation, ANM, Diamant, Sensitivity analysis
Mots-clés : Continuation, MAN, Diamant, Analyse de sensibilité

Author's affiliations:

Isabelle Charpentier ¹

¹ Laboratoire de physique et mécanique des matériaux, UMR 7554, Île du Saulcy, 57045 Metz cedex 1, France

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Isabelle Charpentier. Sensitivity of solutions computed through the Asymptotic Numerical Method. Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 788-793. doi : 10.1016/j.crme.2008.09.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.09.003/

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