Volume 14, Number 1, January-March 2008
|Page(s)||160 - 191|
|Published online||21 September 2007|
Removing holes in topological shape optimization
MIP, UMR 5640, INSA Département de Mathématiques Complexe Scientifique de Rangueil, 31077 Toulouse Cedex 4, France; firstname.lastname@example.org
2 ENIT-LAMSIN et Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia; email@example.com
Revised: 2 June 2006
Revised: 19 July 2006
The gradient based topological optimization tools introduced during the last 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 remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving 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.
Mathematics Subject Classification: 49Q10 / 49Q12 / 74P05 / 74P10 / 74P15
Key words: Topological optimization / topological sensitivity / topological gradient / shape optimization / Stokes equations
© EDP Sciences, SMAI, 2007
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