@article{16339,
  author = {Johannes Haubner and Martin Siebenborn and Michael Ulbrich},
  title = {A Continuous Perspective on Shape Optimization via Domain Transformations},
  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.},
  year = {2021},
  journal = {SIAM Journal of Scientific Computing},
  volume = {43},
  pages = {A1997{\textendash}A2018},
  publisher = {Society for Industrial and Applied Mathematics},
  doi = {10.1137/20M1332050},
}