Fast Summation for Spherical Convolutions

Convolutions on the sphere are important in many aspects of the geosciences, and many unstructured numerical methods make heavy use of them. However, when discretized, these convolutions result in sums that scale as $O(N^2)$ in the number of grid points, which is challenging for scaling to large problem sizes. In this talk, I will present a fast summation technique that allows us to approximate such sums while reducing the complexity from $O(N^2)$ to $O(N\log{N})$ with a spherical tree code that is suitable for a wide range of problems in the geosciences.