A1 Refereed original research article in a scientific journal
Fast Computation of Analytic Capacity
Authors: Nasser, Mohamed M. S.; Green, Christopher C.; Vuorinen, Matti
Publisher: SPRINGER HEIDELBERG
Publishing place: HEIDELBERG
Publication year: 2024
Journal: Computational Methods and Function Theory
Journal name in source: COMPUTATIONAL METHODS AND FUNCTION THEORY
Journal acronym: COMPUT METH FUNCT TH
Number of pages: 28
ISSN: 1617-9447
eISSN: 2195-3724
DOI: https://doi.org/10.1007/s40315-024-00547-2
Web address : https://doi.org/10.1007/s40315-024-00547-2
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457176490
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 & odblac; 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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