Temat: variational inequality - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Topological derivatives for semilinear elliptic equations
Autorzy:: Iguernane, M.
Nazarov, S. A.
Roche, J. R.
Sokolowski, J.
Szulc, K.
Powiązania:: https://bibliotekanauki.pl/articles/907655.pdf
Data publikacji:: 2009
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: optymalizacja kształtu
pochodna topologiczna
nierówność wariacyjna
analiza asymptotyczna
shape optimization
topological derivative
level set method
variational inequality
asymptotic analysis
Opis:: The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L [...] norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 191-205
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Topological sensitivity analysis for a coupled nonlinear problem with an obstacle
Autorzy:: Abdelbari, M.
Nachi, K.
Sokolowski, J.
Powiązania:: https://bibliotekanauki.pl/articles/205653.pdf
Data publikacji:: 2017
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: topological derivative
shape optimization
SteklovPoincaroperator
Signorini problem
variational inequality
Helmholtz equation
coupled partial diﬀerential equations
conical diﬀerential
asymptotic expansions
singular perturbations of geometrical Romains
truncated domain
Opis:: The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-diﬀerential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.
Źródło:: Control and Cybernetics; 2017, 46, 1; 5-25
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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