Fast Summation on the Sphere with Applications to the Barotropic Vorticity Equation

Fast summation refers to a family of techniques for approximating $O(N^2)$ sums in $O(N\log{N})$ or $O(N)$ time. These techniques have traditionally found wide use in astrophysics and electrostatics in calculating the forces in a $N$-body problem. In this work, we present a spherical tree code, and apply it to the problem of efficiently solving the barotropic vorticity equation.