A Cubed Sphere Fast Multipole Method
This work addresses computational challenges in geophysical and fluid dynamics simulations on spherical domains, representing an incremental improvement with a novel grid-based approach.
The authors tackled the problem of efficiently summing pairwise particle interactions on the sphere by developing a new Fast Multipole Method using a cubed sphere grid with barycentric Lagrange interpolation, achieving kernel-independent approximations that require evaluations only at points on the sphere.
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.