OpenCL Based Parallel Algorithm for RBF-PUM Interpolation

We present a parallel algorithm for multivariate Radial Basis Function Partition of Unity Method (RBF-PUM) interpolation. The concurrent nature of the RBF-PUM enables designing parallel algorithms for dealing with a large number of scattered data-points in high space dimensions. To efficiently exploit this concurrency, our algorithm makes use of shared-memory parallel processors through the OpenCL standard. This efficiency is achieved by a parallel space partitioning strategy with linear computational time complexity with respect to the input and evaluation points. The speed of our approach allows for computationally more intensive construction of the interpolant. In fact, the RBF-PUM can be coupled with a cross-validation technique that searches for optimal values of the shape parameters associated with each local RBF interpolant, thus reducing the global interpolation error. The numerical experiments support our claims by illustrating the interpolation errors and the running times of our algorithm.