Shape Optimization for Free Boundary Problems – Analysis and Numerics

Chapter
First Online:
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)

Abstract

In this paper the solution of a Bernoulli type free boundary problem by means of shape optimization is considered. Four different formulations are compared from an analytical and numerical point of view. 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 the discretization of 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.

Keywords

Shape optimization free boundary problems sufficient optimality conditions boundary element method 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Institut für Numerische MathematikTechnische Universität DresdenDresdenGermany
  2. 2.Mathematisches InstitutUniversität BaselBaselSchweiz

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