Shape optimization of systems governed by Bernoulli free boundary problems

In this paper we consider shape optimization of systems, which are governed by external Bernoulli free boundary problems. A pseudo-solid approach for solving discrete free boundary problems is introduced. The solution strategy readily allows us to obtain geometrical sensitivities of the system, in particular the sensitivity of the free boundary. The sensitivity information can then be used to solve, e.g. inverse design problems, where the free boundary is driven towards some target boundary by changing the shape of the other component of the boundary.