A Rescaled Localized Radial Basis Function Interpolation on Non-Cartesian and Nonconforming Grids

In this paper we propose a Rescaled Localized Radial Basis Functions (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from classic RBF interpolation technique, we introduce a rescaling that recovers the partition of unity combined with a new algorithm to select the support of the basis. The proposed rescaling generates a set of basis functions that allows for exact interpolation of constant fields between non-conforming meshes without the use of an extra polynomial term. We also present 2D and 3D 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.