Bengt Fornberg
Dept. of Applied Mathematics
University of Colorado
Boulder, Colorado, USA
Radial basis functions (RBFs) originated in the 1970s as a method for interpolating scattered data. More recently, both our knowledge about RBFs and their range of applications have grown tremendously. They easily generalize to multiple dimensions, handle irregular domains, and can be spectrally accurate both for interpolation and for solving PDEs. We will discuss some key properties of RBF interpolants and also a couple of computational algorithms for RBFs which bypass ill-conditioning issues in the particularly interesting case of relatively flat basis functions. In the context of solving PDEs, RBF based methods generalize pseudospectral (PS) methods in allowing irregular geometries and local node refinement.