Shape Optimisation for Bernoulli Free Boundary Problems.

Abstract

The project aims to numerically analyse and computationally solve a PDE-constrained shape optimisation problem, in the case where a solution of the PDE constraint is approximated with the finite element method. The optimisation problem is solved numerically by means of the trust region method. In this work, we use the shape optimisation library Fireshape, which based on the finite element software Firedrake. A test case demonstrates the applicability of the proposed algorithm.