The phase-field method is a powerful tool in computer-aided materials science as it allows for the analysis of the time-spatial evolution of microstructures on the mesoscale. A multi-phase-field model is adopted to run numerical simulations in two different areas of scientific interest: Polycrystalline thin films growth and the ferromagnetic shape memory effect. FFT-techniques, norm conservative integration and RVE-methods are necessary to make the coupled problems numerically feasible.