A Fast Tree Algorithm for Electric Field Calculation in Electrical Discharge Simulations

摘要

The simulation of electrical discharges has been attracting a great deal ofattention. In such simulations, the electric field computation dominates thecomputational time. In this paper, we propose a fast tree algorithm that helpsto reduce the time complexity from $O(N^2)$ (from using direct summation) to$O(N\log N)$. The implementation details are discussed and the time complexityis analyzed. A rigorous error estimation shows the error of the tree algorithmdecays exponentially with the number of truncation terms and can be controlledadaptively. Numerical examples are presented to validate the accuracy andefficiency of the algorithm.