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

Chair of Mathematical Optimization

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

19 Scopus citations

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.

Original language	English
Title of host publication	Constrained Optimization and Optimal Control for Partial Differential Equations
Publisher	Springer Basel
Pages	257-275
Number of pages	19
ISBN (Electronic)	9783034801331
ISBN (Print)	9783034801324
DOIs	https://doi.org/10.1007/978-3-0348-0133-1
State	Published - 1 Jan 2012

Keywords

Goal-oriented error estimation
Navier-stokes equations
PDE-constrained optimization
Shape optimization

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10.1007/978-3-0348-0133-1

Cite this

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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. p. 257-275.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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

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AU - Lindemann, Florian

AU - Ulbrich, Michael

AU - Ulbrich, Stefan

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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.

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KW - Navier-stokes equations

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KW - Shape optimization

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BT - Constrained Optimization and Optimal Control for Partial Differential Equations

PB - Springer Basel

ER -

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

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Keywords

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