Complex simulation models in the engineering sciences usually consist of many submodels, e.g. from different physical disciplines (“multiphysics”) or different scales in time and place (“multiscale” and “multirate”).

For example, often devices can be simulated sufficiently accurate as electrical circuits, i.e., by lumped network models. However, the increasing frequencies and the decreasing size forces designers to account for wave propagation effects, eddy-currents, ferromagnetic saturation and hysteresis as well as multiphysical phenomenae. Complicated material behavior, e.g. superconductivity make the mathematical model even more challenging. Some of those effects can be represented by order-reduced equivalent models that are embedded in an electrical circuit but other require fully coupled simulations.

The representation of field-dependent nonlinearities, hysteresis and multiphysical effects is not straightforward. Complex 3D field models are required, e.g. discretized with classical finite elements (FEM) or isogeometric analysis (IGA). Therefore hybrid field/circuit models are a relevant research topic on its own.