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

An extension of the well‐known Neville–Aitken's algorithm for interpolation on the Grassmann manifold Gm(ℝn) in the framework of parametric model order reduction is presented. Interpolation points on Gm(ℝn) are the subspaces spanned by bases obtained by Proper Orthogonal Decomposition of availa...

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Vydáno v:	International journal for numerical methods in fluids Ročník 93; číslo 7; s. 2421 - 2442
Hlavní autoři:	Mosquera, Rolando, El Hamidi, Abdallah, Hamdouni, Aziz, Falaize, Antoine
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Bognor Regis Wiley Subscription Services, Inc 01.07.2021 Wiley
Témata:	Algorithms Center of gravity Computational fluid dynamics Grassmann manifold Inflow Interpolation Manifolds (mathematics) Model reduction Neville interpolation algorithm Physics Proper Orthogonal Decomposition Reduced order models Subspaces Vortex shedding Interpolation algorithms Proper orthogonal decompositions Asymptotic complexity Computational fluid dynamics Wakes Von Karman vortices Parametric modeling Reduced order models Lid-driven cavities Interpolation points
ISSN:	0271-2091, 1097-0363
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Shrnutí:	An extension of the well‐known Neville–Aitken's algorithm for interpolation on the Grassmann manifold Gm(ℝn) in the framework of parametric model order reduction is presented. Interpolation points on Gm(ℝn) 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. – Our algorithm is based only on the notion of geodesic barycenter of two points in the manifold. – Unlike iterative algorithms, based on the notion of Karcher's barycenter, our algorithm is explicit. – It does not require any reference point and numerical results are relevant with respect to accuracy while the asymptotic complexity is comparable to the state of the art.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0271-2091 1097-0363
DOI:	10.1002/fld.4981