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Fast computation of analytic capacity
Nasser, Mohamed M. S. Green, Christopher C. Vuorinen, Matti
Nasser, Mohamed M. S.
Green, Christopher C.
Vuorinen, Matti
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2024
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Article
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Keywords
30C40,30C85,65E05,65R20,Ahlfors map,Analytic capacity,Boundary integral equation,Multiply connected domain,Special functions,Szeg? kernel
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Citation
Nasser, M.M.S., Green, C.C., Vuorinen, M. Fast computation of analytic capacity. (2024). Computational Methods and Function Theory. DOI: 10.1007/s40315-024-00547-2
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 Szeg? 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. © The Author(s) 2024.
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Springer Science and Business Media Deutschland GmbH
Journal
Computational Methods and Function Theory
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1617-9447