Authors | J. Haubner, M. Siebenborn and M. Ulbrich |
Title | A Continuous Perspective on Shape Optimization via Domain Transformations |
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Status | Published |
Publication Type | Journal Article |
Year of Publication | 2021 |
Journal | SIAM Journal of Scientific Computing |
Volume | 43 |
Issue | 3 |
Pagination | A1997–A2018 |
Publisher | Society 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. |
DOI | 10.1137/20M1332050 |
Citation Key | 28237 |