Autor: Dambrine, M. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Influence of a boundary perforation on the Dirichlet energy
Autorzy:: Dambrine, M.
Vial, G.
Powiązania:: https://bibliotekanauki.pl/articles/970142.pdf
Data publikacji:: 2005
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: pochodna kształtu
pochodna topologiczna
singular shape perturbation
shape derivatives
topological derivatives
multi-scale asymptotic expansion
Opis:: We consider some singular perturbations of the boundary of a smooth domain. Such domain variations are not differentiable within the classical theory of shape calculus. We mimic the topological asymptotic and we derive an asymptotic expansion of the shape function in terms of a size parameter. The two-dimensional case of the Dirichlet energy is treated in detail. We give a full theoretical proof as well as a numerical confirmation of the results.
Źródło:: Control and Cybernetics; 2005, 34, 1; 117-136
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On stability analysis in shape optimisation : critical shapes for Neumann problem
Autorzy:: Dambrine, M.
Sokolowski, J.
Żochowski, A.
Powiązania:: https://bibliotekanauki.pl/articles/970525.pdf
Data publikacji:: 2003
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: optymalizacja kształtu
analiza stabilności
gradient kształtu
shape optimisation
stability analysis
shape gradient
shape Hessian
Opis:: The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then, the new estimates for the shape Hessian are derived in order to overcome the classical two norms-discrepancy well know in control problems, Malanowski (2001). In the context of shape optimization, the situation is similar compared to control problems, actually, the shape Hessian can be coercive only in the norm strictly weaker with respect to the norm of the second order differentiability of the shape functional. In addition, it is shown that an appropriate regularization makes possible the stability of critical shapes.
Źródło:: Control and Cybernetics; 2003, 32, 3; 503-528
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

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