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

TL;DR

This paper presents a fast multipole method-based framework for accurate, efficient 3D photoionization simulation in streamer discharges, outperforming PDE-based models in accuracy and scalability.

Contribution

It introduces a kernel-independent fast multipole method for photoionization calculation, improving accuracy and computational efficiency in 3D streamer discharge simulations.

Findings

Fast multipole method reduces numerical error significantly.

Method achieves stable performance across different domains and pressures.

Scalable to 1280 cores for large-scale simulations.

Abstract

This paper focuses on the three-dimensional simulation of the photoionization in streamer discharges, and provides a general framework to efficiently and accurately calculate the photoionization model using the integral form. The simulation is based on 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.