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• City of GrazOn Shape Sensitivity Analysis of the Cost Functional Without Shape Sensitivity of the State Variable

By Karl–franzens Universität Graz, Technische Universität Graz, Medizinische Universität Graz, H. Kasumba and K. KunischH. Kasumba and K. Kunisch

Abstract

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

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Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.412.1356
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