Philip Herbert: Thursday, 06th March 2025 at 10:30
Abstract: In this talk, we discuss a novel method in PDE constrained shape optimisation. While it is known that many shape optimisation problems have a solution, finding the solution, or an approximation of the solution, may prove non-trivial. A typical approach to minimisation is to use a first order method; this raises questions when handling shapes – what is a shape derivative, where does it live? It happens to be convenient to define the derivatives as linear functionals on $W^{1,\infty}$. We present an analysis of this in a discrete setting along with the existence of directions of steepest descent. Several numerical experiments will be considered and extensions discussed.
