Optimization of piecewise smooth shapes under uncertainty using the example of Navier--Stokes flow
Authors
- Geiersbach, Caroline
ORCID: 0000-0002-6518-7756 - Suchan, Tim
- Welker, Kathrin
2020 Mathematics Subject Classification
- 49Q12 49K20 53C15
Keywords
- Shape optimization, product manifold, augmented Lagrangian, stochastic optimization, uncertainties
DOI
Abstract
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.
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