POD basis interpolation via Inverse Distance Weighting on Grassmann manifolds

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.