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

  • M. Heinkenschloss
  • E. W. Sachs
Part of the ISNM International Series of Numerical Mathematics book series (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.

1991 Mathematics Subject Classification

49M15 

Key words and phrases

Optimal control bound constraints projected Newton method phase field model 

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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • M. Heinkenschloss
    • 1
  • E. W. Sachs
    • 2
  1. 1.Interdisciplinary Center for Applied Mathematics and Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.FB IV - MathematikUniversität TrierTrierFederal Republic of Germany

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