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Optimal Control of Allen-Cahn Systems

  • Luise BlankEmail author
  • M. Hassan Farshbaf-Shaker
  • Claudia Hecht
  • Josef Michl
  • Christoph Rupprecht
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)

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.

Keywords

Allen-Cahn system Parabolic obstacle problems Linear elasticity Mathematical programs with complementarity constraints Optimality conditions Trust-Region-Newton method 

Mathematics Subject Classification (2010)

Primary 49J40 Secondary 49K20 49J20 49M15 74P99 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Luise Blank
    • 1
    Email author
  • M. Hassan Farshbaf-Shaker
    • 2
  • Claudia Hecht
    • 1
  • Josef Michl
    • 3
  • Christoph Rupprecht
    • 1
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Weierstraß-Institut, Mohrenstr. 39BerlinGermany
  3. 3.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany

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