WIAS Preprint No. 1906, (2013)

Optimal control of Allen--Cahn systems



Authors

  • Blank, Luise
  • Farshbaf Shaker, Mohammad Hassan
  • Hecht, Claudia
  • Michl, Josef
  • Rupprecht, Christoph

2010 Mathematics Subject Classification

  • 49J40 49K20 49J20 49M15 74P99

Keywords

  • Allen-Cahn system, parabolic obstacle problems, linear elasticity, mathematical programs with complementarity constraints, optimality conditions, Trust-Region-Newton method

Abstract

Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented.

Appeared in

  • Trends in PDE Constrained Optimization, G. Leugering, P. Benner et al., eds., vol. 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 11--26

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