Fast and accurate computation of the logarithmic capacity of compact sets

DOI10.1007/s40315-017-0207-1zbMath1381.65026arXiv1507.05793OpenAlexW2532373555MaRDI QIDQ1689818

Mohamed M. S. Nasser, Jörg Liesen, Olivier Sète

Publication date: 17 January 2018

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05793

zbMATH Keywords

numerical exampleboundary integral equationlogarithmic capacityconformal mapChebyshev constanttransfinite diameterCantor middle third setlemniscatic domain

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Capacity and harmonic measure in the complex plane (30C85) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Schwarz-Christoffel-type mappings (30C30)

Related Items

Condenser capacity and hyperbolic perimeter ⋮ Computation of conformal invariants ⋮ Isoperimetric properties of condenser capacity ⋮ Numerical computation of the capacity of generalized condensers ⋮ Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals ⋮ Logarithmic capacity under holomorphic motions in higher dimensions ⋮ Computing the logarithmic capacity of compact sets having (infinitely) many components with the charge simulation method ⋮ Minimal degree rational open up mappings and related questions ⋮ Conformal invariants in simply connected domains ⋮ SERIES SOLUTION OF LAPLACE PROBLEMS ⋮ Geometrical logarithmic capacitance ⋮ Condenser capacity and hyperbolic diameter ⋮ On capacity computation for symmetric polygonal condensers ⋮ Numerical computation of Mityuk's function and radius for circular/radial slit domains ⋮ Conformal capacity and polycircular domains ⋮ Level sets of potential functions bisecting unbounded quadrilaterals

Uses Software

• Schwarz-Christoffel
• SC Toolbox
• FMMLIB2D

Cites Work

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