共形容量与多圆域
Conformal capacity and polycircular domains
摘要：
本文研究多连通平面区域的数值共形映射，这些区域的边界由多个圆弧并组成，称为多圆区域。本文计算了由多圆域定义的凝聚体的共形容量。实验误差估计提供的计算能力，并在可能的情况下，离散化细化下的收敛速率进行了分析。计算的主要成分是两种计算方法，一方面是边界积分方程法结合快速多极子方法，另一方面是$hp$ -有限元方法。这两种方法所得结果具有较高的精度。
英文摘要：
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by polycircular domains. Experimental error estimates are provided for the computed capacity and, when possible, the rate of convergence under refinement of discretisation is analysed. The main ingredients of the computation are two computational methods, on one hand the boundary integral equation method combined with the fast multipole method and on the other hand the $hp$-FEM method. The results obtained with these two methods agree with high accuracy.
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