Accurate and efficient calculation of photoionization in streamer discharges using fast multipole method

Abstract

This paper focuses on fast and accurate three-dimensional simulation of the photoionization in streamer discharges based on the classical integral model derived by Zheleznyak et al. The simulation is based on the integral form of the photoionization rate with the kernel-independent fast multipole method. The accuracy of this method is studied quantitatively for different domains and various pressures in comparison with other existing models based on partial differential equations (PDEs). The comparison indicates the numerical error of the fast multipole method is much smaller than those of other PDE-based methods, with the reference solution given by direct numerical integration. Such accuracy can be achieved with affordable computational cost, and its performance in both efficiency and accuracy is quite stable for different domains and pressures. Meanwhile, the simulation accelerated by the fast multipole method exhibits good scalability using up to 1280 cores, which shows its capability of three-dimensional simulations using parallel (distributed) computing. The difference of the proposed method and other efficient approximations are also studied in a three-dimensional dynamic problem where two streamers interact.