Helmut Harbrecht:

Analytical and numerical methods in shape optimization

The present paper is intented to overview on analytical and numerical methods in shape optimization. We compute and analyse the shape Hessian in order to distinguish well-posed and ill-posed shape optimization problems. We introduce different discretization techniques of the shape and present existence and convergence results of approximate solutions in case of well-posedness. Finally, we survey on the efficient numerical solution of the state equation, including finite and boundary element methods as well as fictitious domain methods.

Erstveröffentlichung: Preprint No. 305, Berichtsreihe des SFB 611, Universität Bonn, 2006.

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[Thu Feb 19 18:56:37 2009]

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