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Numerical Solution of a Constrained Control Problem for a Phase Field Model

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Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 118))

Abstract

A phase field model is considered for an evolution process which describes the phase change from solid to liquid. The process is controlled by inputs which are uniformly bounded. The objective is that the phase and the temperature follow certain desired functions as close as possible with a cost term for the control. The necessary optimality conditions of first order are formulated for this control problem. These conditions include projections which make the application of Newton’s method difficult. We present an approach to circumvent this difficulty and obtain an algorithm which is very efficient numerically. The numerical examples indicate that the required time to solve the problem with control constraints is of the same magnitude as for the unconstrained problem.

This work was supported in part by AFOSR under Grant F49620-93-1-0280 while the author was a visiting scientist at the Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University.

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Author information

Authors and Affiliations

  1. Interdisciplinary Center for Applied Mathematics and Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0123, USA

    M. Heinkenschloss

  2. FB IV - Mathematik, Universität Trier, D-54286, Trier, Federal Republic of Germany

    E. W. Sachs

Authors
  1. M. Heinkenschloss
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  2. E. W. Sachs
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universitat Graz, Heinrichstrasse 36, A-8010, Graz, Austria

    W. Desch  & F. Kappel  & 

  2. Fachbereich Mathematik, Technische Universitat Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    K. Kunisch

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© 1994 Springer Basel AG

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Heinkenschloss, M., Sachs, E.W. (1994). Numerical Solution of a Constrained Control Problem for a Phase Field Model. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8530-0_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9666-5

  • Online ISBN: 978-3-0348-8530-0

  • eBook Packages: Springer Book Archive

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