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 between the proposed method and other efficient approximations is also studied in a three-dimensional dynamic problem where two streamers interact.

中文翻译：

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使用快速多极方法准确有效地计算流光放电中的光电离

本文着重于基于 Zheleznyak 等人推导出的经典积分模型，对流光放电中的光电离进行快速准确的三维模拟。模拟基于光电离率的积分形式，采用与核无关的快速多极方法。与基于偏微分方程 (PDE) 的其他现有模型相比，该方法的准确性在不同域和各种压力下进行了定量研究。比较表明快速多极方法的数值误差比其他基于偏微分方程的方法的数值误差小得多，参考解由直接数值积分给出。这样的精度可以通过负担得起的计算成本来实现，并且其在效率和精度方面的性能对于不同的领域和压力都非常稳定。同时，通过快速多极方法加速的仿真在使用多达 1280 个内核时表现出良好的可扩展性，显示了其使用并行（分布式）计算进行三维仿真的能力。在两个拖缆相互作用的三维动态问题中，还研究了所提出的方法与其他有效近似方法之间的差异。