Least-Squares Projected Models for Non-Intrusive Affinization of Reduced Basis Methods

Abstract

Reduced-basis methods (RBMs) constitute a promising technique for delivering numerical solutions of parameterized PDEs in real time and with reasonable accuracy. The most significant drawback of RBMs is the requirement of parametric affinity, a condition that only very trivial problems satisfy. Without parametric affinity, the reduced model cannot be quickly assembled in the online stage. The most common solution to this issue is to establish a form of approximate parametric affinity. However, most methods for doing so are highly intrusive: they require in-depth expert knowledge of the problem to be solved, of the high-fidelity simulation software for solving it, or both. It is often impossible to adapt a high-fidelity software package for RBMs without significant source-code edits. We present an approach for approximate affinization based on least-squares projected quantities over a predetermined function space. We contend that this offers a method for affinization with minimal impact, which we demonstrate by producing linear elastic RBMs for components using two widely different simulation software packages, without source code edits and with no significant expert knowledge.