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Condenser capacity and hyperbolic perimeter

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journal contribution
submitted on 2023-10-17, 09:05 and posted on 2023-10-18, 04:36 authored by Mohamed M.S. Nasser, Oona Rainio, Matti Vuorinen

We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of condensers (𝐺,𝐸) where 𝐺 is a simply connected domain in the complex plane and 𝐸 is a compact subset of 𝐺. Due to conformal invariance, our main tools are the hyperbolic geometry and functionals such as the hyperbolic perimeter of 𝐸. Our computational experiments demonstrate, for instance, sharpness of established inequalities. In the case of model problems with known analytic solutions, very high precision of computation is observed.

Other Information

Published in: Computers & Mathematics with Applications
License: http://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.1016/j.camwa.2021.11.016

Funding

Open Access funding provided by the Qatar National Library

History

Language

  • English

Publisher

Elsevier

Publication Year

  • 2022

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License

Institution affiliated with

  • Qatar University
  • College of Arts and Sciences - QU