AuthorsJ. Haubner, M. Siebenborn and M. Ulbrich
TitleA Continuous Perspective on Shape Optimization via Domain Transformations
AfilliationScientific Computing
Project(s)No Simula project
StatusPublished
Publication TypeJournal Article
Year of Publication2021
JournalSIAM Journal of Scientific Computing
Volume43
Issue3
PaginationA1997–A2018
PublisherSociety for Industrial and Applied Mathematics
Abstract

In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes, a reference domain is introduced, and it is optimized over a set of admissible transformations. The focus is on the choice of the set of transformations, which we motivate from a continuous perspective. In order to guarantee local injectivity of the admissible transformations, we enrich the optimization problem by a nonlinear constraint. Numerical results for drag minimization of Stokes flow are presented.

DOI10.1137/20M1332050
Citation Key28237