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（无限）多个“小”分支组成的紧集的对数容量。该方法允许为每个分支仅使用单个电荷点。因此，与基于边界离散化的方法（例如，我们之前在[Liesen, Sète, Nasser, 2017]中提出的方法）相比，所得方法在保持非常高精度的同时显著提高了效率。我们研究了CSM中产生的线性代数系统的性质，并展示了如何利用预处理迭代法高效求解这些系统，其中矩阵-向量乘积通过快速多极子方法计算。我们通过广义康托尔集和康托尔尘示例说明了该方法的应用。