Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow

Christian Brandenburg; Florian Lindemann; Michael Ulbrich; Stefan Ulbrich

doi:10.1007/978-3-0348-0133-1

Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow

Christian Brandenburg, Florian Lindemann, Michael Ulbrich, Stefan Ulbrich

Lehrstuhl für Mathematische Optimierung

Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

18 Zitate (Scopus)

Abstract

We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.

Originalsprache	Englisch
Titel	Constrained Optimization and Optimal Control for Partial Differential Equations
Herausgeber (Verlag)	Springer Basel
Seiten	257-275
Seitenumfang	19
ISBN (elektronisch)	9783034801331
ISBN (Print)	9783034801324
DOIs	https://doi.org/10.1007/978-3-0348-0133-1
Publikationsstatus	Veröffentlicht - 1 Jan. 2012

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10.1007/978-3-0348-0133-1

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keywords = "Goal-oriented error estimation, Navier-stokes equations, PDE-constrained optimization, Shape optimization",

author = "Christian Brandenburg and Florian Lindemann and Michael Ulbrich and Stefan Ulbrich",

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Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow. / Brandenburg, Christian; Lindemann, Florian; Ulbrich, Michael et al.
Constrained Optimization and Optimal Control for Partial Differential Equations. Springer Basel, 2012. S. 257-275.

Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

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T1 - Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow

AU - Brandenburg, Christian

AU - Lindemann, Florian

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AU - Ulbrich, Stefan

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Y1 - 2012/1/1

N2 - We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.

AB - We present an approach to shape optimization which is based on transformation to a reference domain with continuous adjoint computations. This method is applied to the instationary Navier-Stokes equations for which we discuss the appropriate setting and discuss Fréchet differentiability of the velocity field with respect to domain transformations. Goal-oriented error estimation is used for an adaptive refinement strategy. Finally, we give some numerical results.

KW - Goal-oriented error estimation

KW - Navier-stokes equations

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BT - Constrained Optimization and Optimal Control for Partial Differential Equations

PB - Springer Basel

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Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow

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