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.

翻译：快速求和是指一类将$O(N^2)$阶求和问题近似为$O(N\log{N})$或$O(N)$时间复杂度的技术。这类技术在天体物理学和静电学中计算$N$体问题中的作用力时已有广泛应用。本文提出一种球形树编码，并将其应用于高效求解正压涡度方程的问题。