Finite element discretisations are beneficial for models with complicated geometries, non-linearities and eddy current effects. Full size finite element models of technical devices, however, often suffer from unacceptably large simulation times. In this paper, only subdomains in which important local effects occur, are discretised by finite elements. Other parts of the device can be modelled up to a sufficient accuracy by appropriate boundary conditions and circuits coupled to the finite element formulation. The resulting hybrid approach is particularly suited for technical modelling and yields small discrete models. The shorter computation times allow the models to be embedded in iterative design procedures and optimisation routines that inevitably incorporate a large number of finite element evaluations.