Topological optimization and inverse problems

  • Lidia Jackowska-Strumiłło Technical University of Łódź
  • Jan Sokołowski Universite Henri Poincaré
  • Antoni Żochowski Systems Research Institute of the Polish Academy of Sciences

Abstract

The topological derivative of an arbitrary shape functional is introduced in [29] for 2D elasticity. The optimality conditions for general shape optimization problems are established in [30] using the shape variations including boundary and topology variations. The topology variations result in the presence of topological derivatives in the necessary conditions for optimality. In the present paper we derive the necessary optimality conditions for a class of shape optimization problems. The topological variations of shape functionals are used for the numerical solution of inverse problems. The numerical method uses neural networks. The results of computations confirm the convergence of the method.

Keywords

topological derivative, shape optimization, optimality conditions, artificial neural network, shape inverse problem, nucleation of openings,

References

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Published
Jan 27, 2023
How to Cite
JACKOWSKA-STRUMIŁŁO, Lidia; SOKOŁOWSKI, Jan; ŻOCHOWSKI, Antoni. Topological optimization and inverse problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 10, n. 2, p. 163-176, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1085>. Date accessed: 13 nov. 2024.
Section
Articles