WIAS Preprint No. 3037, (2023)

Optimization of piecewise smooth shapes under uncertainty using the example of Navier--Stokes flow


  • Geiersbach, Caroline
    ORCID: 0000-0002-6518-7756
  • Suchan, Tim
  • Welker, Kathrin

2020 Mathematics Subject Classification

  • 49Q12 49K20 53C15


  • Shape optimization, product manifold, augmented Lagrangian, stochastic optimization, uncertainties




We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape manifolds with multi-shape calculus, which provides a novel framework for the handling of piecewise smooth shapes. This multi-shape calculus is applied to a shape optimization problem where shapes serve as obstacles in a system governed by steady state incompressible Navier--Stokes flow. Numerical experiments use our recently developed stochastic augmented Lagrangian method and we investigate the choice of algorithmic parameters using the example of this application.

Download Documents