A level set method in shape and topology optimization for variational inequalities

Piotr Fulmański; Antoine Laurain; Jean-Francois Scheid; Jan Sokołowski

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 3, page 413-430
  • ISSN: 1641-876X

Abstract

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The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

How to cite

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Fulmański, Piotr, et al. "A level set method in shape and topology optimization for variational inequalities." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 413-430. <http://eudml.org/doc/207847>.

@article{Fulmański2007,
abstract = {The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.},
author = {Fulmański, Piotr, Laurain, Antoine, Scheid, Jean-Francois, Sokołowski, Jan},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {shape optimization; level set method; asymptotic analysis; variational inequality; topological derivative},
language = {eng},
number = {3},
pages = {413-430},
title = {A level set method in shape and topology optimization for variational inequalities},
url = {http://eudml.org/doc/207847},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Fulmański, Piotr
AU - Laurain, Antoine
AU - Scheid, Jean-Francois
AU - Sokołowski, Jan
TI - A level set method in shape and topology optimization for variational inequalities
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 3
SP - 413
EP - 430
AB - The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.
LA - eng
KW - shape optimization; level set method; asymptotic analysis; variational inequality; topological derivative
UR - http://eudml.org/doc/207847
ER -

References

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