A Cubed Sphere Fast Multipole Method

This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange interpolation on a quadtree composed of cubed sphere grid cells. The scheme is kernel-independent and requires kernel evaluations only at points on the sphere. Results are presented for the Poisson and biharmonic equations on the sphere, barotropic vorticity equation on a rotating sphere, and self-attraction and loading potential in tidal calculations. A tree code version is also described for comparison, and both schemes are tested in serial and parallel calculations.