Numerical approximation of optimal convex shapes

Sören Bartels; Gerd Wachsmuth

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arXiv · 1810.10735

Numerical approximation of optimal convex shapes

Sören Bartels·Gerd Wachsmuth

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Abstract

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem. Moreover, we prove the convergence of discretizations in two-dimensional situations. A numerical algorithm is devised that iteratively solves the discrete formulation. Numerical experiments show that optimal convex shapes are generally non-smooth and that three-dimensional problems require an appropriate relaxation of the convexity condition.

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Sören Bartels, Gerd Wachsmuth. 2018-10-25. Numerical approximation of optimal convex shapes. https://arxiv.org/abs/1810.10735

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