Sample selection based on sensitivity analysis in parameterized model order reduction

Abstract

Modeling of scientific or engineering applications often yields high-dimensional dynamical systems due to techniques of computer-aided-design, for example. Thus a model order reduction is required to decrease the dimensionality and to enable an efficient numerical simulation. In addition, methods of parameterized model order reduction (pMOR) are often used to preserve the physical or geometric parameters as independent variables in the reduced order models. We consider linear dynamical systems in the form of ordinary differential equations. In the domain of the parameters, often samples are chosen to construct a reduced order model. For each sample point a common technique for model order reduction can be applied to compute a local basis. Moment matching or balanced truncation are feasible, for example. A global basis for pMOR can be constructed from the local bases by a singular value decomposition. We investigate approaches for an appropriate selection of a finite set of samples. The transfer function of the dynamical system is examined in the frequency domain, and our focus is on moment matching techniques using the Arnoldi procedure. We use a sensitivity analysis of the transfer function with respect to the parameters as a tool to select sample points. Simulation results are shown for two examples.