论文标题
共形能力和多圆形结构域
Conformal capacity and polycircular domains
论文作者
论文摘要
我们研究了由有限的许多圆形弧的工会组成的乘积平面结构域的数值共形映射，即所谓的多圆形域。我们计算由多圆形结构域定义的冷凝器的共形能力。为计算能力提供了实验误差估计，并在可能的情况下分析了离散化细化后的收敛速率。计算的主要成分是两种计算方法，一方面是边界积分方程方法与快速多极方法结合使用，另一方面是$ HP $ -FEM方法。用这两种方法获得的结果与高精度一致。
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.
