A level-set method for shape optimization
[Une méthode de lignes de niveaux pour l'optimisation de forme]
Allaire, Grégoire1 ; Jouve, François1 ; Toader, Anca-Maria2
1 Centre de mathématiques appliquées, École polytechnique, 91128 Palaiseau, France
2 CMAF, Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa, Portugal
Comptes Rendus. Mathématique, Tome 334 (2002) no. 12, pp. 1125-1130.

Nous proposons une méthode de lignes de niveaux pour l'optimisation de la forme de structures élastiques. Notre approche combine la méthode des lignes de niveaux d'Osher et Sethian et la dérivée classique de formes. Bien que cette méthode ne soit pas spécifiquement conçue pour faire de l'optimisation topologique, elle permet très facilement les changements de topologie de la forme d'une structure pour des fonctions objectifs très générales. Son coût en temps de calcul est modéré puisqu'il s'agit d'une méthode numérique de capture de formes sur un maillage eulérien fixe.

We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.

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DOI : 10.1016/S1631-073X(02)02412-3
Allaire, Grégoire 1 ; Jouve, François 1 ; Toader, Anca-Maria 2

1 Centre de mathématiques appliquées, École polytechnique, 91128 Palaiseau, France
2 CMAF, Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa, Portugal 
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Allaire, Grégoire; Jouve, François; Toader, Anca-Maria. A level-set method for shape optimization. Comptes Rendus. Mathématique, Tome 334 (2002) no. 12, pp. 1125-1130. doi : 10.1016/S1631-073X(02)02412-3. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02412-3/

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