# Computational comparison of surface metrics for PDE constrained shape optimization

arXiv: https://arxiv.org/abs/1509.08601 · HTML: https://mlsanity.com/paper/1509.08601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)

## Abstract (arXiv)

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.