Document ESAIM: COCV, Vol. 14, N°1, pp. 160-191
DOI: 10.1051/cocv:2007045
Removing holes in topological shape optimization
Philippe Guillaume1 and Maatoug Hassine21 MIP, UMR 5640, INSA Département de Mathématiques Complexe Scientifique de Rangueil, 31077 Toulouse Cedex 4, France; philippe.guillaume@insa-toulouse.fr
2 ENIT-LAMSIN et Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia; maatoug.hassine@enit.rnu.tn
(Received December 14, 2005. Revised June 2 and July 19, 2006. Published online September 21, 2007.)
Abstract
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