A Linear View on Shape Optimization
Optimization and Control
2022-03-15 v1
Abstract
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view are highlighted and a novel linear version of the second shape derivative is proposed leading to particular algorithms of shape Newton type.
Cite
@article{arxiv.2203.07175,
title = {A Linear View on Shape Optimization},
author = {Stephan Schmidt and Volker H. Schulz},
journal= {arXiv preprint arXiv:2203.07175},
year = {2022}
}