Physical structures and processes are modeled by dynamical systems in many application areas, such as the design of very large-scale integration chips or large power systems. Since these dynamical systems can become very large, the essential simulation before production may consume hours or days of computing time. Hence there is need for efficient approaches that limit the computing time while preserving the accuracy. In this paper it will be shown how specialized eigen value methods and model order reduction techniques can be used to perform fast and accurate simulations of large dynamical systems. Results will be illustrated by numerical experiments with realistic examples.