Fast Computation of Analytic Capacity

Pub Date : 2024-06-07 DOI:10.1007/s40315-024-00547-2
Mohamed M. S. Nasser, Christopher C. Green, Matti Vuorinen
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Abstract

A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman–Stein integral equation to compute the Szegő kernel and then the value of the derivative of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity.

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快速计算分析能力
本文提出了一种边界积分方程方法,用于快速计算复平面内紧凑集合的解析能力。该方法基于使用 Kerzman-Stein 积分方程计算 Szegő 核,然后计算无穷远点处的 Ahlfors 地图导数值。所提出的方法可用于具有平滑和片状平滑边界的域。当与保角映射相结合时,该方法可用于紧凑狭缝集。我们列举了几个数值示例来证明所提方法的效率。我们恢复了一些已知的精确结果,并证实了分析能力的猜想亚可加性属性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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