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Séminaire des doctorants - 21 septembre 2016

Matteo Giacomini (CMAP) - On the volumetric expression of the shape gradient

Salle de conférence du CMAP - 15h00

Shape optimization problems may be viewed as PDE-constrained optimization problems of a shape-dependent functional, the domain being the optimization variable and the PDE being the constraint. We are interested in gradient-based methods for the solution of this class of problems. In this talk, we discuss several expressions of the so-called shape gradient and we focus on the comparison between its surface and its volumetric expressions. After recalling an analytical result on the shape gradient of a shape-dependent functional with a constraint given by an elliptic PDE, we discuss the minimization of the compliance under a volume constraint within the framework of linear elasticity. In particular, the pure displacement and the dual mixed formulations of the linear elasticity problem are considered and a preliminary qualitative comparison of the resulting surface and volumetric expressions of the shape gradient is proposed through some numerical simulations.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46