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

• DOI: 10.1002/fld.4981
• Publication Date: 2021-03-20T11:59:10Z
• Authors: Rolando Mosquera; Abdallah El Hamidi; Aziz Hamdouni; Antoine Falaize
• Keywords: Interpolation; Manifold (fluid mechanics)

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