SHAPE OPTIMIZATION FOR FREE BOUNDARY PROBLEMS

Harbrecht, Helmut; Eppler, K.

In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.

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Harbrecht, Helmut / Eppler, K.: SHAPE OPTIMIZATION FOR FREE BOUNDARY PROBLEMS. 2010.

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