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(NlogN) 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.