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In this paper we propose a rescaled localized radial basis function (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from the classical RBF interpolation technique, we introduce a rescaling that allows for exact interpolation of constant fields between nonconforming meshes without the use of an extra polynomial term. We also present two-dimensional and three-dimensional numerical examples on arbitrary finite element meshes to show that the RL-RBF interpolation leads to accurate results, fast evaluation, and easy parallelization of the algorithm. All the computations are carried out using the open source finite element library LifeV.
Quentin Christian Becker, Mike Yan Michelis
Fabio Nobile, Yoshihito Kazashi