We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows to use just a single charge point for each component. The resulting method therefore is significantly more efficient than methods based on discretizations of the boundaries (for example, our own method presented in [Liesen, S\`ete, Nasser, 2017]), while maintaining a very high level of accuracy. We study properties of the linear algebraic systems that arise in the CSM, and show how these systems can be solved efficiently using preconditioned iterative methods, where the matrix-vector products are computed using the Fast Multipole Method. We illustrate the use of the method on generalized Cantor sets and the Cantor dust.

翻译：我们应用电荷模拟法(CSM)来计算由(绝对)许多“小型”组件组成的紧凑组群的对数能力。这种应用允许对每个部件只使用一个单一的充电点。因此,由此产生的方法比基于边界分解的方法(例如,我们自己的方法在[Liesen,S<unk> ete,Nasser,2017]中介绍)效率要高得多,同时保持非常高的精确度。我们研究CSM中产生的线性代数系统的特性,并展示如何使用先决条件的迭接法有效解决这些系统,即使用快速多极法计算矩阵-矢量产品。我们举例说明了在通用的Cantor装置和Cantor粉尘中使用的方法。</s>