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October  2019, 12(6): 1743-1759. doi: 10.3934/dcdss.2019115

## POD basis interpolation via Inverse Distance Weighting on Grassmann manifolds

 Laboratoire LaSIE, Université de La Rochelle, Avenue M. Crépeau, 17042 La Rochelle, France

* Corresponding author: Abdallah El Hamidi

Received  February 2018 Revised  April 2018 Published  November 2018

An adaptation of the Inverse Distance Weighting (IDW) method to the Grassmann manifold is carried out for interpolation of parametric POD bases. Our approach does not depend on the choice of a reference point on the Grassmann manifold to perform the interpolation, moreover our results are more accurate than those obtained in [7]. In return, our approach is not direct but iterative and its relevance depends on the choice of the weighting functions which are inversely proportional to the distance to the parameter. More judicious choices of such weighting functions can be carried out via kriging technics [23], this is the subject of a work in progress.

Citation: Rolando Mosquera, Aziz Hamdouni, Abdallah El Hamidi, Cyrille Allery. POD basis interpolation via Inverse Distance Weighting on Grassmann manifolds. Discrete & Continuous Dynamical Systems - S, 2019, 12 (6) : 1743-1759. doi: 10.3934/dcdss.2019115
##### References:

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##### References:
Geometrical properties of the flow around a circular cylinder
Isovalue of the velocity magnitude for Re = 180 at the first snapshot
Influence of the power $p$ of the IDW-G interpolation on the prediction of the drag and lift for Reynolds number $Re = 160$ and $Re = 190$
Comparison of the drag and lift coefficients obtained by the two interpolations methods IDW-G and Grassmann and those obtained with the full model for Re = 140 and 160
Comparison of the drag and lift coefficients obtained by the two interpolations methods IDW-G and Grassmann and those obtained with the full model for Re = 170 and 190
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