On the ersatz material approximation in level-set methods

Marc Dambrine; Djalil Kateb

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

  • Volume: 16, Issue: 3, page 618-634
  • ISSN: 1292-8119

Abstract

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The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys.194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the ersatz material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.

How to cite

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Dambrine, Marc, and Kateb, Djalil. "On the ersatz material approximation in level-set methods." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 618-634. <http://eudml.org/doc/250750>.

@article{Dambrine2010,
abstract = { The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys.194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the ersatz material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function. },
author = {Dambrine, Marc, Kateb, Djalil},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Shape optimization; stability; second order shape derivative; level-set method; ersatz material approximation; shape optimization; ersatz material approximation},
language = {eng},
month = {7},
number = {3},
pages = {618-634},
publisher = {EDP Sciences},
title = {On the ersatz material approximation in level-set methods},
url = {http://eudml.org/doc/250750},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Dambrine, Marc
AU - Kateb, Djalil
TI - On the ersatz material approximation in level-set methods
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/7//
PB - EDP Sciences
VL - 16
IS - 3
SP - 618
EP - 634
AB - The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys.194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the ersatz material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.
LA - eng
KW - Shape optimization; stability; second order shape derivative; level-set method; ersatz material approximation; shape optimization; ersatz material approximation
UR - http://eudml.org/doc/250750
ER -

References

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