Case Study: Parametrized Reduction Using Reduced-Basis and the Loewner Framework

Abstract

In this case study, we compare two methods for model reduction of parametrized systems, namely, Reduced-Basis and Loewner rational interpolation. While having the same goal of constructing reduced-order models for large-scale parameter-dependent systems, the two methods follow fundamentally different approaches. On the one hand, the well known Reduced-Basis method takes a time domain approach, using offline snapshots of the full-order system combined with a rigorous error bound. On the other hand, the recently introduced Loewner matrix framework takes a frequency-domain approach that constructs rational interpolants of transfer function measurements, and has the flexibility of allowing different reduced-orders for each of the frequency and parameter variables. We apply the two methods to a parametrized partial differential equation modeling the transient temperature evolution near the surface of a cylinder immersed in fluid. Then, we compare the resulting reduced-order models with the full-order finite element system by running both time- and frequency-domain simulations.