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Main Title: Domain optimization for the Navier-Stokes equation by an embedding domain method
Author(s): Slawig, Thomas
Type: Research Paper
Abstract: Domain optimization problems for the two-dimensional stationary flow of incompressible linear-viscous fluids, i.e. the Navier-Stokes equations, are studied. An embedding domain technique which provides an equivalent formulation of the problem on a fixed domain is introduced. Existence of a solution to the domain optimization problem and Fréchet differentiability with respect to the variation of the domain of tracking type cost functionals for the velocity field are proved. A simply computable formula for the derivative of the cost functional is presented. Numerical examples show the advantages of the embedding domain method and the reliability of the derivative formula.
Subject(s): domain optimization
Navier-Stokes equation
embedding domain method
fixed domain
Issue Date: 26-Oct-1998
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 49Q10 Optimization of shapes other than minimal surfaces
49J50 Fréchet and Gateaux differentiability
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1998, 600
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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