On the ersatz material approximation in level-set methods
Université de Pau et des Pays de l'Adour; CNRS UMR 5142, LMA, France. firstname.lastname@example.org
2 Université de Technologie de Compiègne; EA 2222, LMAC, France.
Revised: 15 March 2009
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 ersatz material approximation [Allaire et al., J. Comput. Phys. 194 (2004) 363–393], 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 ersatz material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.
Mathematics Subject Classification: 49Q10 / 34A55 / 49Q12
Key words: Shape optimization / stability / second order shape derivative / level-set method / ersatz material approximation
© EDP Sciences, SMAI, 2009