  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.
