Motion planning of solid-liquid interfaces in crystal growth processes

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Autor/in:
Erscheinungsjahr:
2009
Medientyp:
Text
Schlagworte:
  • Inverse problems
  • Solidification
  • Biological tissue
  • Inverse Problems
  • Boundary Value Problems
  • Heat Conduction
  • Crystal growth
  • Motion planning
  • Free boundary control
  • Inverse problems
  • Solidification
  • Biological tissue
  • Inverse Problems
  • Boundary Value Problems
  • Heat Conduction
Beschreibung:
  • We present an optimal control approach for the solidification process of a melt in a container. The process is described by a two phase Stefan problem including flow driven by convection and Lorentz forces. The free boundary (interface between the two phases) is modelled as a graph. We control the motion of the free boundary using the temperature on the container wall and/or the Lorentz forces. The control goal consists in tracking a prescribed evolution of the free boundary. We achieve this goal by minimizing a appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method with step size control, where the gradient of the cost functional is expressed in terms of the adjoint variables. Numerical examples are presented which illustrate the performance of the method. © 2009 American Institute of Physics.
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  • info:eu-repo/semantics/closedAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/d97a306d-c518-45c1-b655-46b52c1cc596