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Removing holes in topological shape optimization

Published online by Cambridge University Press:  21 September 2007

Philippe Guillaume  and
Maatoug Hassine
Philippe Guillaume
Affiliation:
MIP, UMR 5640, INSA Département de Mathématiques Complexe Scientifique de Rangueil, 31077 Toulouse Cedex 4, France; philippe.guillaume@insa-toulouse.fr
Maatoug Hassine
Affiliation:
ENIT-LAMSIN et Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia; maatoug.hassine@enit.rnu.tn
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Abstract

The gradient based topological optimization tools introduced during thelast ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remainunchanged, at least during the topological phase of the optimizationalgorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not forimproving the cost function. Then, two numerical examples are presented:the first one compares topological optimization with standard shape optimization, and the second one, issued from a lake oxygenation problem, illustrates the use of the new asymptotic expansion.


Keywords

Topological optimizationtopological sensitivitytopological gradientshape optimizationStokes equations
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 1 , January 2008 , pp. 160 - 191
Copyright
© EDP Sciences, SMAI, 2007

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