Computation of capacity

DOI10.1090/S0025-5718-07-01941-2zbMath1113.65026OpenAlexW1972140029MaRDI QIDQ3433767

Jérémie Rostand, Thomas Ransford

Publication date: 2 May 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01941-2

zbMATH Keywords

numerical examplesCantor setlogarithmic capacitymatrix gameHölder continuity property

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items

Numerical computation of the capacity of generalized condensers ⋮ Linkage of logarithmic capacity in potential theory and degenerate scale in the BEM for two tangent discs ⋮ Computation of logarithmic capacity ⋮ Fast and accurate computation of the logarithmic capacity of compact sets ⋮ Logarithmic capacity under holomorphic motions in higher dimensions ⋮ Computing the logarithmic capacity of compact sets having (infinitely) many components with the charge simulation method ⋮ Revisit of logarithmic capacity of line segments and double-degeneracy of BEM/BIEM ⋮ Pluripotential numerics ⋮ Hölder exponents of Green's functions of Cantor sets ⋮ Orthogonal polynomials of equilibrium measures supported on Cantor sets ⋮ Cantor polynomials and some related classes of OPRL ⋮ Computation of weighted capacity ⋮ Computation of capacity via quadratic programming ⋮ SERIES SOLUTION OF LAPLACE PROBLEMS ⋮ Computation of Chebyshev polynomials for union of intervals ⋮ Computable Complex Analysis

Uses Software

• DCUHRE
• Schwarz-Christoffel
• SC Toolbox

Cites Work

• Uniformly perfect sets and the Poincaré metric
• Complex dynamics
• Iterated function systems, capacity and Green's functions
• Extremal polynomials associated with a system of curves in the complex plane
• On an extension of the definition of transfinite diameter and some applications.
• On the Implementation of a Primal-Dual Interior Point Method
• Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
• Algorithm 698: DCUHRE
• Computing Logarithmic Capacity with Linear Programming
• Green's Functions for Multiply Connected Domains via Conformal Mapping
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