07-6   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Helmut Harbrecht:

A Newton method for Bernoulli's free boundary problem in three dimensions

The present paper is dedicated to the numerical solution of Bernoulli's free boundary problem in three dimensions. We reformulate the given free boundary problem as a shape optimization problem and compute the shape gradient and Hessian of the given shape functional. To approximate the shape problem we apply a Ritz-Galerkin discretization. The necessary optimality condition is solved by Newton's method. All information of the state equation, required for the optimization algorithm, are derived by boundary integral equations which we solve numerically by a fast wavelet Galerkin scheme. Numerical results confirm that the proposed Newton method yields an efficient algorithm to solve the considered class of problems.

Erstveröffentlichung: Preprint No. 321, Berichtsreihe des SFB 611, Universität Bonn, 2007.

Keywords: free boundary problem, shape calculus, Newton method, boundary integral equation, wavelets

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[Thu Feb 19 18:56:37 2009]