alexa A Dirichlet–Neumann cost functional approach for the Bernoulli problem
Mathematics

Mathematics

Journal of Applied & Computational Mathematics

Author(s): A Ben Abda, G H Peichl, M Sayeh

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The Bernoulli problem is rephrased into a shape optimization problem. In particular, the cost function, which turns out to be a constitutive law gap functional, is borrowed from inverse problem formulations. The shape derivative of the cost functional is explicitly determined. The gradient information is combined with the level set method in a steepest descent algorithm to solve the shape optimization problem. The efficiency of this approach is illustrated by numerical results for both interior and exterior Bernoulli problems.

This article was published in Journal of Engineering Mathematics and referenced in Journal of Applied & Computational Mathematics

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