Adaptive strategies to fast multipole method in photoionisation calculations for streamer discharges

Abstract

Recently, a new framework to compute the photoionisation rate in streamer discharges accurately and efficiently using the integral model and the fast multipole method (FMM) was presented. This paper further improves the efficiency of this framework with adaptive strategies. The adaptive strategies are based on the magnitude of radiation and the electric field during the streamer propagation, and are applied to the selection of the source and target points. The accuracy and efficiency of this adaptive FMM are studied quantitatively for different domain sizes, pressures and adaptive criteria, in comparison with some existing efficient approaches to compute the photoionisation. It is shown that appropriate adaptive strategies reduce the calculation time of the FMM greatly, and maintain the high accuracy that the numerical error is still much smaller than other methods based on partial differential equations. The performance of the proposed adaptive method is also studied for a three-dimensional positive streamer interacting problem with a plasma cloud, which shows that the FMM with proper adaptive strategies is even faster than the partial differential equation based methods with efficient boundary conditions for the ionisation calculation.