Geodesic
Minisymposium Optimisation de forme: avant-propos
Alain Dervieux1 ; Jan Sokolowski2
1 INRIA Project-Team, 2004 route des lucioles, BP 93, 06902 Sophia-Antipolis, FRANCE
2 Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-lès-Nancy cedex, FRANCE
ESAIM. Proceedings, Tome 22 (2008), pp. 156-161.

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Starting from Hadamard's and Garabedian's works, the shape optimisation was a part of classical calculus of variations. The analysis of free boundary problem problems is performed as well in the framework of the shape optimization. The most advanced applications are now in computer aided design of optimal shapes in many domains including car and aircraft industries. In the 80's, J.-L. Lions suggested to use the adjoint state equations for aerodynamics shape optimization problems, which leads to efficient numerical methods. Optimal Control for shapes is now popular domain in Applied Mathematics and Engineering. New shape gradients were proposed for numerical solutions of such problems (deformation velocity of J. Céa and J.-P. Zolésio; topological derivatives of shape functionals of J. Sokolowski and A. Zochowski, M. Masmoudi based on the asymptotic analysis of the Russian school) and the adjoint states are presently routinely used for numerical methods of shape optimization. Today, parameterization is an important issue for general representation and for computational efficiency. Topological derivatives were recently combined with Level Set methods. The foreword of this minisymposium review shortly these advances and try to identify some unsolved directions. Then the first communication presents this approach for a variational inequality. The aerodynamics-oriented methods are studied in three subsequent communications. First, a Free-Form-Deformation is combined with an adaptative Bézier representation of the boundary. Second, a multilevel optimisation relying on Bézier representation is studied. Then the impact of flow and functional smoothness for supersonic flows is analysed.
DOI : 10.1051/proc:072219

Alain Dervieux 1 ; Jan Sokolowski 2

1 INRIA Project-Team, 2004 route des lucioles, BP 93, 06902 Sophia-Antipolis, FRANCE
2 Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-lès-Nancy cedex, FRANCE 
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Alain Dervieux; Jan Sokolowski. Minisymposium Optimisation de forme: avant-propos. ESAIM. Proceedings, Tome 22 (2008), pp. 156-161. doi : 10.1051/proc:072219. http://geodesic.mathdoc.fr/articles/10.1051/proc:072219/

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