Getting state-space models from FEM simulations

Finite element based modeling is one of the most powerful computational tools currently available. Amongst others a possible drawback could be the computation duration time, that can be expected at transient nonlinear problems, or at more simple problems with a large time span. One of the possible solutions is trying simplify the FEM model into a lower order system without losing its characteristic behavior. In this paper we study the possibilities of state-space models as candidate lower order systems of FEM models using three different approaches: (1) Using the state-space model export function of Comsol itself; (2) Using a system identification tool to retrieve a black box state-space model; (3) using inverse modeling to get a lumped parameter state-space model.
Our methodology was to start with a simple benchmark in Comsol, compare the three above mentioned approaches and proceed by adding more complexity into the next benchmark. Thus obtaining results for different benchmarks.
We conclude all approaches are capable of significantly reduce computation duration time without loss of accuracy. Comparing the three approaches from a physical point of view, the grey-box model is preferable because its parameters (state-space matrices) have a physical meaning and therefore parameters studies can be done without the necessity to simulate the FEM model over and over again. Finally, the reader should notice that no general conclusions can be obtained from this rather limited study.