Numerical techniques for different time scales in electric circuit simulation

The simulation of integrated circuits demands an increasing amount of computational resources, since systems become more and more complex and parasitic effects are included to a larger extent. However, the number of active elements keeps relatively small: less than 10%. In other settings digital and analog circuits are coupled, which yields systems with largely differing time scales. We will discuss two techniques, which are adapted to those cases. One approach is based on multirate Rosenbrock-Wanner schemes, the other leads to a PDE-model for driven oscillators.