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Title
On shape sensitivity analysis of the cost functional without shape sensitivity of the state variable
AuthorKasumba, Henry ; Kunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
Control and Cybernetics, Warszawa, 2011, Vol. 40, Issue 4, page 989-1017
PublishedPaństwowe Wyd. Nauke
LanguageEnglish
Document typeJournal Article
Keywords (EN)Shape derivative / Navier-Stokes equations / Cost functional
ISSN0324-8569
URNurn:nbn:at:at-ubg:3-537 Persistent Identifier (URN)
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 The work is publicly available
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Abstract (English)

A general framework for calculating shape derivatives for domain optimizationproblems with partial differential equations as constraints is presented. Thefirst order approximation of the cost with respect to the geometry perturbation isarranged in an efficient manner that allows the computation of the shape derivativeof the cost without the necessity to involve the shape derivative of the statevariable. In doing so, the state variable is only required to be Lipschitz continuouswith respect to geometry perturbations. Application to shape optimization with theNavier-Stokes equations as PDE constraint is given.