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On the ersatz material approximation in level-set methods

Published online by Cambridge University Press:  31 July 2009

Marc Dambrine  and
Djalil Kateb
Marc Dambrine
Affiliation:
Université de Pau et des Pays de l'Adour; CNRS UMR 5142, LMA, France. marc.dambrine@univ-pau.fr
Djalil Kateb
Affiliation:
Université de Technologie de Compiègne; EA 2222, LMAC, France.
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Abstract

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.

Keywords

Shape optimizationstabilitysecond order shape derivativelevel-set methodersatz materialapproximation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 3 , July 2010 , pp. 618 - 634
Copyright
© EDP Sciences, SMAI, 2009

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