Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Levesley, J. and Hough, D. M. (1995) Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain. Advances in Computational Mathematics, 3 (1-2). pp. 115-135. ISSN 1572-9044 doi: 10.1007/BF03028363

Abstract/Summary

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.