Temat: shape derivatives - 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

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Skocz do pozycji: 2.

Tytuł:: Second derivatives and sufficient optimality conditions for shape funetionals
Autorzy:: Eppler, K.
Powiązania:: https://bibliotekanauki.pl/articles/206712.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: optimal shape design
second directional derivatives
sufficient optimality conditions
Opis:: For sorne heuristic approaches to boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for these approaches the functionals are Frechet-differentiable in some sense, because at least a local embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.
Źródło:: Control and Cybernetics; 2000, 29, 2; 485-511
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Boundary integral representations of second derivatives in shape optimization
Autorzy:: Eppler, Karsten
Powiązania:: https://bibliotekanauki.pl/articles/729245.pdf
Data publikacji:: 2000
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: optimal shape design
fundamental solution
boundary integral equation
second-order derivatives
optimality conditions
Opis:: For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral representation of the second derivative of the objective is possible. Basing on this, one easily obtains that the second derivative contains only normal components for stationary domains, i.e. for domains, satisfying the first order necessary condition for a free optimum. Moreover, the nature of the second derivative is discussed, which is helpful for the investigation of sufficient optimality conditions.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 1; 63-78
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

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