Collocation-based model order reduction: analysis and applications
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We consider a novel reduced-order modeling strategy called collocation Model Order Reduction (cMOR), designed as an alternative to more classic projection-based Model Order Reduction (pMOR). The cMOR approach maintains the typical online-offline paradigm of pMOR, with an initial offline phase for constructing a reduced basis from solution snapshots. However, in the online phase, while pMOR computes the reduced solution through projection onto a reduced basis, cMOR instead solves the governing equations at a small set of collocation points, identified via hyper-reduction techniques. Within this setting, we present a theoretical analysis of the stability and error of the method, and we validate our findings through numerical illustrations. These results confirm the robustness and accuracy of cMOR, while its formulation ensures straightforward integration into existing simulation workflows.
