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Topological Methods in Nonlinear Analysis

Topological optimization via cost penalization
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Topological optimization via cost penalization

Authors

  • Cornel Marius Murea
  • Dan Tiba

Keywords

Geometric optimization, optimal design, topological variations, optimal control methods, discrete gradient

Abstract

We consider general shape optimization problems governed by Dirichlet boundary value problems. The proposed approach may be extended to other boundary conditions as well. It is based on a recent representation result for implicitly defined manifolds, due to the authors, and it is formulated as an optimal control problem. The discretized approximating problem is introduced and we give an explicit construction of the associated discrete gradient. Some numerical examples are also indicated.

References

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M.R. Nicolai and D. Tiba, Implicit functions and parametrizations in dimension three: generalized solutions, Discrete Contin. Dyn. Syst. 35 (2015), no. 6, 2701–2710.

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D. Tiba, A penalization approach in shape optimization, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 96 (2018), no. 1, A8, DOI: 10.1478/AAPP.961A8.

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Published

2019-11-09

How to Cite

1.
MUREA, Cornel Marius and TIBA, Dan. Topological optimization via cost penalization. Topological Methods in Nonlinear Analysis. Online. 9 November 2019. Vol. 54, no. 2B, pp. 1023 - 1050. [Accessed 4 July 2025].
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