Numerical approximation of optimal convex shapes
Optimization and Control
2018-10-26 v1
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.
Cite
@article{arxiv.1810.10735,
title = {Numerical approximation of optimal convex shapes},
author = {Sören Bartels and Gerd Wachsmuth},
journal= {arXiv preprint arXiv:1810.10735},
year = {2018}
}