Model order reduction and parameterization of nonlinear numerical models

We describe techniques of model order reduction (MOR) for weakly nonlinear finite difference and finite element (FE) models. In our approach we combine the parameter identification based on linearized systems for a behavioral description of weakly nonlinear effects by means of a Taylor series expansion. To get manageable nonlinear behavioral models, we use projection based on MOR-methods (on the base of Krylov subspace and singular perturbation approaches for the linear case). We therefore take advantage of using the linearized model description in nonlinear MOR without the necessity of having an explicit formulation of the nonlinearities - such providing, for example, nonlinear MOR techniques to simulations with commercial FE software. We demonstrate the applicability of the methods on a time depending of heat transfer including material and thermal radiation nonlinearities.