On the algebraic and geometric structure of RB methods

Abstract

RB methods are revisited from both an algebraic and a geometric standpoint. A number of relationships between the Galerkin RB approximation (as well as least-squares RB approximation) and the Galerkin high-fidelity approximation (3.11) are highlighted, for the purpose of illustrating, in a more fitting way and from a different perspective, the mathematical structure underpinning RB methods. The key role played by the transformation matrix in defining orthogonal and oblique projections is emphasized.