# 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

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topFulmański, 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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## Citations in EuDML Documents

top- Alexander Khludnev, Jan Sokołowski, Katarzyna Szulc, Shape and topological sensitivity analysis in domains with cracks
- Andrzej Myśliński, Topology optimization of systems governed by variational inequalities
- Mohamed Iguernane, Serguei A. Nazarov, Jean-Rodolphe Roche, Jan Sokolowski, Katarzyna Szulc, Topological derivatives for semilinear elliptic equations
- Andrzej Myśliński, Topology optimization of quasistatic contact problems

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