A linear and spectral model has recently been developed [1], describing the self-consistent wave-particle interaction in a gyrotron oscillator. The spectral approach, compared to commonly used time-evolution approaches, has the possibility to describe all of the stable and unstable modes, respectively, with negative and positive growth rates. Moreover, this approach is numerically efficient and thus appropriate for parameter scans or start-up scenario studies. The model has been successfully benchmarked against real experiments for gyrotron cavity interaction, in particular concerning start-up scenario studies. In order to study backward-wave instabilities in smooth-wall beam ducts, the numerical model has been recently extended to include a higher order finite element discretization. The model, its numerical implementation and simulation results for high power gyrotrons as well as first results for smooth-wall beam ducts will be presented.