  In this paper we show a simplified optimisation approach for free boundary
problems in arbitrary space dimensions. This approach is mainly based on an
extended operator splitting which allows a decoupling of the domain deformation
and solving the remaining partial differential equation. First we give a short
introduction to free boundary problems and the problems occurring in
optimisation. Then we introduce the extended operator splitting and apply it to
a general minimisation subject to a time-dependent scalar-valued partial
differential equation. This yields a time-discretised optimisation problem
which allows us a quite simple application of adjoint-based optimisation
methods. Finally, we verify this approach numerically by the optimisation of a
flow problem (Navier-Stokes equation) and the final shape of a Stefan-type
problem.
