A Bilevel Shape Optimization Problem for the Exterior Bernoulli Free Boundary Problem

Henry Kasumba*, Karl Kunisch and Antoine Laurain

A bilevel shape optimization problem with the exterior Bernoulli free boundary problem as lower-level problem and the control of the free boundary as the upper-level problem is considered. Using the shape of the inner boundary as the control, we aim at reaching a specific shape for the free boundary. A rigorous sensitivity analysis of the bilevel shape optimization in the infinite-dimensional setting is performed. The numerical realization using two different cost functionals presented to demonstrate the efficiency of the approach.

Mathematics Subject Classification: 35R35 35Q93

Keywords: Bernoulli free boundary problem; shape optimization; multilevel optimization.

Minisymposion: Shape Optimization and Free Boundaries