# Removing holes in topological shape optimization

Philippe Guillaume; Maatoug Hassine

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 14, Issue: 1, page 160-191
- ISSN: 1292-8119

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topGuillaume, Philippe, and Hassine, Maatoug. "Removing holes in topological shape optimization." ESAIM: Control, Optimisation and Calculus of Variations 14.1 (2010): 160-191. <http://eudml.org/doc/90862>.

@article{Guillaume2010,

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.
},

author = {Guillaume, Philippe, Hassine, Maatoug},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Topological optimization; topological sensitivity;
topological gradient;
shape optimization; Stokes equations; topological optimization; topological gradient; shape optimization},

language = {eng},

month = {3},

number = {1},

pages = {160-191},

publisher = {EDP Sciences},

title = {Removing holes in topological shape optimization},

url = {http://eudml.org/doc/90862},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Guillaume, Philippe

AU - Hassine, Maatoug

TI - Removing holes in topological shape optimization

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 14

IS - 1

SP - 160

EP - 191

AB -
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.

LA - eng

KW - Topological optimization; topological sensitivity;
topological gradient;
shape optimization; Stokes equations; topological optimization; topological gradient; shape optimization

UR - http://eudml.org/doc/90862

ER -

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