Fast Summation for Geophysical Fluid Dynamics

Convolutions on the sphere are useful in many geophysical fluid dynamics problems, 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. This work will discuss a fast summation technique that allows us to approximate such sums while reducing the complexity from O(N^2) to O(N). It uses a cubed sphere tree code that is suitable for a wide range of problems that arise in geophysical fluid dynamics, including vorticity dynamics and tidal simulations.