A Cubed Sphere Fast Multipole Method
Abstract
Abstract. 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.
Fields of Study & Subjects
Microwave Engineering and Waveguides
Antenna Design and Analysis
Advanced Antenna and Metasurface Technologies
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Volume
- 48
- Issue
- 4
- Pages
- B671–B697
- Publication date
- 31 July 2026
- Language
- EN