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arXiv · 1603.08235

Shape optimisation with nonsmooth cost functions: from theory to numerics

Kevin Sturm
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Abstract

This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint approach and maximal elliptic regularity. Furthermore we characterise stationary points and show how to compute steepest descent direc- tions theoretically and practically. Finally, we present some numerical results for a simple toy problem and compare them with the smooth case. We also compare the convergence rates and obtain higher rates in the nonsmooth case.

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Kevin Sturm. 2016-03-27. Shape optimisation with nonsmooth cost functions: from theory to numerics. https://arxiv.org/abs/1603.08235

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