论文标题
计算具有电荷仿真方法的（无限）许多组件的紧凑型集合的对数能力
Computing the logarithmic capacity of compact sets having (infinitely) many components with the Charge Simulation Method
论文作者
论文摘要
我们应用电荷仿真方法（CSM），以计算由（无限）许多“小”组件组成的紧凑型集合的对数能力。此应用程序仅允许为每个组件使用一个充电点。因此，最终的方法比基于边界的离散化的方法要高得多（例如，我们自己的方法在[Liesen，Sète，Nasser，2017年）中提出，同时保持非常高的准确性。我们研究了CSM中出现的线性代数系统的性能，并展示了如何使用预处理的迭代方法有效地求解这些系统，其中使用快速多极方法计算矩阵矢量产物。我们说明了该方法在广义的Cantor套装和cantor灰尘上的使用。
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, Sète, 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.
