Computational comparison of surface metrics for PDE constrained shape optimization
Optimization and Control
2021-04-12 v2
Abstract
We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In particular, classical Laplace-Beltrami type based metrics are compared with Steklov-Poincar\'e type metrics. The test problem is the minimization of energy dissipation of a body in a Stokes flow. We therefore set up a quasi-Newton method on appropriate shape manifolds together with an augmented Lagrangian framework, in order to enable a straightforward integration of geometric constraints for the shape. The comparison is focussed towards convergence behavior as well as effects on the mesh quality during shape optimization.
Cite
@article{arxiv.1509.08601,
title = {Computational comparison of surface metrics for PDE constrained shape optimization},
author = {Volker Schulz and Martin Siebenborn},
journal= {arXiv preprint arXiv:1509.08601},
year = {2021}
}