Fast Computation of Analytic Capacity



: Nasser, Mohamed M. S.; Green, Christopher C.; Vuorinen, Matti

Publisher: SPRINGER HEIDELBERG

: HEIDELBERG

: 2024

: Computational Methods and Function Theory

: COMPUTATIONAL METHODS AND FUNCTION THEORY

: COMPUT METH FUNCT TH

: 28

: 1617-9447

: 2195-3724

DOI: https://doi.org/10.1007/s40315-024-00547-2

: https://doi.org/10.1007/s40315-024-00547-2

: 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.

Last updated on 2025-27-01 at 19:19