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

Abstract

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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.


How to cite

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Guillaume, 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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