Divergence-Free RBFs on Surfaces

Abstract

This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface $P \in {\Bbb R}^3$ to samples of such a field taken at scattered sites on P. This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the method on the sphere are included.