On the weak material approximation in level-sets methods.

Marc Dambrine (1) , Djalil Kateb (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a weak material approximation, a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the weak material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.

Mots clés: shape optimization; stability; second order shape derivative; level-set method; weak material approximation

Domaines: Optimisation et contrôle [math.OC]

Marc Dambrine, Djalil Kateb. On the weak material approximation in level-sets methods.. 2008. ⟨hal-00291225v2⟩