Autor: Sokołowski, Jan - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Sensitivity analysis of the Signorini variational inequality
Autorzy:: Sokołowski, Jan
Powiązania:: https://bibliotekanauki.pl/articles/718927.pdf
Data publikacji:: 1987
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:: Banach Center Publications; 1987, 19, 1; 287-299
0137-6934
Pojawia się w:: Banach Center Publications
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On the robustness of the topological derivative for Helmholtz problems and applications
Autorzy:: Leugering, Günter
Novotny, Antonio André
Sokolowski, Jan
Powiązania:: https://bibliotekanauki.pl/articles/2183490.pdf
Data publikacji:: 2022
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: topological derivative
shape optimization
inverse problems
Helmholtz problem
numerical methods
complex variables
Opis:: We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uɛ) with respect to a small hole Bɛ around a given point x0ɛ ∈ Bɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bɛ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.
Źródło:: Control and Cybernetics; 2022, 51, 2; 227--248
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Network optimality conditions
Autorzy:: Osmolovskii, Nikolai P.
Qian, Meizhi
Sokołowski, Jan
Powiązania:: https://bibliotekanauki.pl/articles/31343935.pdf
Data publikacji:: 2023
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: network
optimal control problem
weak local minimum
Pontryagin’s maximum principle
critical cone
quadratic form
second order optimality conditions
Riccati equation
Opis:: Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
Źródło:: Control and Cybernetics; 2023, 52, 2; 129-180
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Shape sensitivity of optimal control for the Stokes problem
Autorzy:: Abdelbari, Merwan
Nachi, Khadra
Sokolowski, Jan
Szulc, Katarzyna
Powiązania:: https://bibliotekanauki.pl/articles/2049935.pdf
Data publikacji:: 2020
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: Stokes equations
optimal control problem
coupled partial diﬀerential equations
shape optimization
shape gradient
Opis:: In this article, we study the shape sensitivity of optimal control for the steady Stokes problem. The main goal is to obtain a robust representation for the derivatives of optimal solution with respect to smooth deformation of the flow domain. We introduce in this paper a rigorous proof of existence of the material derivative in the sense of Piola, as well as the shape derivative for the solution of the optimality system. We apply these results to derive the formulae for the shape gradient of the cost functional; under some regularity conditions the shape gradient is given according to the structure theorem by a function supported on the moving boundary, then the numerical methods for shape optimization can be applied in order to solve the associated optimization problems.
Źródło:: Control and Cybernetics; 2020, 49, 1; 11-40
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Growth control of cracks under contact conditions based on the topological derivative of the Rice’s integral
Autorzy:: da Silva Xavier, Marcel Duarte
Novotny, Antonio André
Sokołowski, Jan
Powiązania:: https://bibliotekanauki.pl/articles/1839141.pdf
Data publikacji:: 2019
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: Rice’s integral
Griffith’s criterion
Eshelby’s tensor
topological derivative
Opis:: In the present paper we propose a simple method for dealing with growth control of cracks under contact type boundary conditions on their lips. The aim is to find a mechanism for decreasing the energy release rate of cracked components, which means increasing their fracture toughness. The method consists in minimizing a shape functional defined in terms of the Rice’s integral, with respect to the nucleation of hard and/or soft inclusions, according to the information provided by the associated topological derivative. Based on Griffith’s energy criterion, this simple strategy allows for an increase in fracture toughness of the cracked component. Since the problem is non-linear, the domain decomposition technique, combined with the Steklov-Poincaré pseudo-differential boundary operator, is used to obtain the sensitivity of the associated shape functional with respect to the nucleation of a small circular inclusion with different material property from the background. Then, the obtained topological derivatives are used to indicate the regions, where the controls should be positioned in order to solve the minimization problem we are dealing with. Finally, a numerical example is presented showing the applicability of the proposed methodology.
Źródło:: Control and Cybernetics; 2019, 48, 2; 307-323
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki