A levelset method in shape and topology optimization for variational inequalities

Piotr Fulmanski (1) , Antoine Laurain (2) , Jean-Francois Scheid (2, 3) , Jan Sokolowski (2)

1 Faculty of Mathematics [Lodz]
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

Levelset method is used for shape optimization of the energy functional for Signorini problem. The topological derivatives are employed for the topology variations in the form of small holes. Numerical results confirm that the method is efficient and gives better results compared to the classical shape optimization techniques.

Mots clés: shape optimization; topological derivative; levelset method; variational inequality; asymptotic analysis

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Piotr Fulmanski, Antoine Laurain, Jean-Francois Scheid, Jan Sokolowski. A levelset method in shape and topology optimization for variational inequalities. International Journal of Applied Mathematics and Computer Science, 2007, 17 (3), pp.413-430. ⟨10.2478/v10006-007-0034-z⟩. ⟨hal-00092000⟩