Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Space-Time Newton-Multigrid Strategies for Nonstationary Distributed and Boundary Flow Control Problems

Authors : Michael Hinze, Michael Köster, Stefan Turek

Published in: Trends in PDE Constrained Optimization

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper considers a Newton-type solver strategy for optimal flow control problems using space-time multigrid solution techniques. Based on the standard Newton approach for optimal control, a space-time multigrid preconditioner is derived and numerically analysed for distributed and boundary control.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter A-Priori Error Bounds for Finite Element Approximation of Elliptic Optimal Control Problems with Gradient Constraints
next chapter Convergence of Adaptive Finite Elements for Optimal Control Problems with Control Constraints
Literature
1.
R.E. Bank, T.F. Dupond, An optimal order process for solving finite element equations. Math. Comput. 36(153), 35–51 (1981)CrossRefMATH
2.
3.
A. Borzi, V. Schulz, Computational Optimization of Systems Governed by Partial Differential Equations (SIAM, Philadelphia, 2011)CrossRef
4.
5.
M.D. Gunzburger, Perspectives in Flow Control and Optimization (SIAM, Philadelphia, 2003). ISBN:089871527XMATH
6.
7.
W. Hackbusch, Die schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art. Beiträge zur numerischen Mathematik, 9, 47–62 (1981)MATH
8.
W. Hackbusch, Numerical solution of linear and nonlinear parabolic optimal control problems, in Optimization and Optimal Control, eds. by A. Auslender, W. Oettli, J. Stoer. Lecture Notes in Control and Information Science, vol. 30 (Springer, Berlin/New York, 1981), pp. 179–185
9.
W. Hackbusch, Multi-Grid Methods and Applications. Springer Series in Computational Mathematics (Springer, Berlin, 1985). ISBN 3-540-12761-5
10.
M. Hinze, Optimal and instantaneous control of the instationary Navier–Stokes equations. Habilitation thesis, Institut für Numerische Mathematik, Technische Universität Dresden, 2000
11.
M. Hinze, M. Köster, S. Turek, A hierarchical space-time solver for distributed control of the Stokes equation. Preprint SPP1253-16-01, SPP1253, 2008
12.
M. Hinze, M. Köster, S. Turek. A space-time multigrid solver for distributed control of the time-dependent Navier–Stokes system. Preprint SPP1253-16-02, SPP1253, 2008
13.
M. Hinze, M. Köster, S. Turek, A hierarchical space-time solver for optimal distributed control of fluid flow, 2009. Proceedings of the Conference on Modeling, Simulation and Optimization of Complex Processes, Heidelberg, Accepted 21–25 July 2008
14.
V. John, G. Matthies, Higher order finite element discretizations in a benchmark problem for incompressible flows. Int. J. Numer. Methods Fluids 37, 885–903 (2001)CrossRefMATH
15.
M. Köster, A hierarchical flow solver for optimisation with PDE constraints. PhD thesis, TU Dortmund, Lehrstuhl III für Angewandte Mathematik und Numerik, 2011. Slightly corrected version with an additional appendix concerning prolongation/restriction
16.
Metadata
Title
Space-Time Newton-Multigrid Strategies for Nonstationary Distributed and Boundary Flow Control Problems
Authors
Michael Hinze
Michael Köster
Stefan Turek
Copyright Year
2014
Book
Trends in PDE Constrained Optimization

Print ISBN: 978-3-319-05082-9

Electronic ISBN: 978-3-319-05083-6

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05083-6_24