Comptes Rendus
no. 10
Partial differential equations/Calculus of variations
Higher-order topological sensitivity analysis for the Laplace operator
[Analyse de sensibilité topologique d'ordre supérieur pour l'opérateur de Laplace]

Présenté par : Olivier Pironneau

Maatoug Hassine1 ; Khalifa Khelifi1
1 Monastir University, FSM, 5019 Monastir, Tunisia
Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 993-999.

Dans ce papier, on donne une analyse de sensibilité pour l'opérateur de Laplace par rapport à des perturbations géométriques de type Dirichlet. On pésente deux résultats. Le premier concerne l'influence de la perturbation géométrique sur la solution du problème de Laplace. On dérive une formule de représentation asymptotique d'ordre supérieur décrivant le comportement de la solution perturbée en fonction de la taille de la perturbation. Le deuxième concerne les dérivées d'une fonction de forme par rapport à la modification de la topologie du domaine. On donne un développement asymtotique topologique d'ordre supérieur valable pour une grande classe de fonctions de forme.

This paper deals with higher-order topological sensitivity analysis for the Laplace operator with respect to the presence of a Dirichlet geometry perturbation. Two main results are presented in this work. In the first one, we discuss the influence of the considered geometry perturbation on the Laplace solution. The second one is devoted to the higher-order topological derivatives. We derive a higher-order topological sensitivity analysis for a large class of shape functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.09.002
Maatoug Hassine 1 ; Khalifa Khelifi 1

1 Monastir University, FSM, 5019 Monastir, Tunisia 
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Maatoug Hassine; Khalifa Khelifi. Higher-order topological sensitivity analysis for the Laplace operator. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 993-999. doi : 10.1016/j.crma.2016.09.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.002/

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