Generalization of the Neville–Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

Abstract

AbstractAn extension of the well‐known Neville–Aitken's algorithm for interpolation on the Grassmann manifold in the framework of parametric model order reduction is presented. Interpolation points on are the subspaces spanned by bases obtained by Proper Orthogonal Decomposition of available solutions associated with the chosen parameter sampling. The Neville–Aitken's algorithm is performed recursively via the geodesic barycenter of two points. Three CFD applications are presented: (i) the Von Karman vortex shedding street, (ii) the lid‐driven cavity with inflow and (iii) the flow induced by a rotating solid. Numerical results are relevant with respect to accuracy while the asymptotic complexity is comparable to the state of the art.