WIAS Preprint No. 1792, (2013)

Shape optimization for a sharp interface model of distortion compensation



Authors

  • Sturm, Kevin
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Hömberg, Dietmar

2010 Mathematics Subject Classification

  • 49Q10 35Q74 74N15

Keywords

  • Distortion, phase transition, shape optimisation, speed method, transmission problem

Abstract

We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.

Appeared in

  • Comput. Optim. Appl., 64 (2016) pp. 557--588 under the title ``Distortion compensation as a shape optimisation problem for a sharp interface model''

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