Fast algorithm for computing forces between $n$ point in the plane I have a set of distinct particles $\\{z_k\\}_{k=1}^n\subseteq\mathbb{R}^2$ with dynamics $$\dot{z_k} = \sum_{k'\not= k}V(z_k-z_{k'}),$$ where $V$ is a repelling Yukawa potential: $$V(z) = \frac{\alpha}{|z|}e^{-\beta |z|}.$$ I want to numerically solve the equations. A naïve approach has complexity $O(n^2)$, but since the potential decays very rapidly I think there might exists a trick that gives us a faster approximate solution. Also I guess this problem has a more abstract formulation, like a graph theory formulation, so that we can reduce it to more known problems

This paper seems quite relevant:

> A Fast Adaptive Multipole Algorithm for Calculating Screened Coulomb (Yukawa) Interactions, _Journal of Computational Physics_ Volume 151, Issue 1, 1 May 1999, Pages 212-241