Abstract The accurate calculation of the electrostatic forces between charged particles requires a reliable representation of the emerging electric field. To this end, two principle formulations are available, namely Coulomb's and Gauss' laws. While both approaches are in this specific case mathematically equivalent, the numerical solution of Gauss' law on a grid is contaminated by a spatial discretization error. In this paper, we explore under which conditions this error depreciates the computed results of the particle dynamics. More specifically, we introduce a length-scale of the electrostatic interaction which serves as a base to evaluate the required grid resolution. Also, according to our numerical study, this error reduces in case the particle dynamics is contact dominated. Furthermore, we introduce a computationally efficient hybrid scheme which combines the advantages of both formulations and examine in which situations its accuracy is superior to schemes based on the numerical solution of Gauss' law.

中文翻译：

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关于带电粒子间静电力数值计算的准确性

摘要 带电粒子之间静电力的准确计算需要对新兴电场的可靠表示。为此，有两个基本公式可用，即库仑定律和高斯定律。虽然这两种方法在这种特定情况下在数学上是等效的，但高斯定律在网格上的数值解会受到空间离散化误差的影响。在本文中，我们探讨了在哪些条件下此错误会降低粒子动力学的计算结果。更具体地说，我们引入了静电相互作用的长度尺度，作为评估所需网格分辨率的基础。此外，根据我们的数值研究，如果粒子动力学是接触主导的，则该误差会减小。此外，