Shape sensitivity of optimal control for the Stokes problem

• Autorzy: Abdelbari Merwan , Nachi Khadra , Sokolowski Jan , Szulc Katarzyna
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Stokes equation; optimal control problem; coupled partial differential equations; shape optimization; shape gradient

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2020
• Tom: Vol. 49, No. 1
• Strony: 11--40
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Abdelbari Merwan

• Université Oran1, Ahmed Ben Bella, Laboratoire de Mathématique et ses applications BP 1524, El M’naouer, Oran, Algérie
• Université Hassiba Ben Bouali, Département de Mathématiques, Chlef, Algérie

autor

Nachi Khadra

• Université Oran1, Ahmed Ben Bella, Laboratoire de Mathématique et ses applications BP 1524, El M’naouer, Oran, Algérie

autor

Sokolowski Jan

• Université de Lorraine-Nancy, Institut Elie Cartan, Laboratoire de Mathématiques, B.P. 239, 54506, Vandoeuvre lès Nancy cedex, France
• Systems Research Institute of the Polish Academy of Sciences Newelska 6, 01-447 Warsaw, Poland
• Departamento de Computa，cão Científica, Centro de Informática, Universidade Federal da Paraíba, Rua dos Escoteiros s/n, Mangabeira, João Pessoa, PB 58058-600, Brasil

autor

Szulc Katarzyna

• Systems Research Institute of the Polish Academy of Sciences Newelska 6, 01-447 Warsaw, Poland

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).