Abstract
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.
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Chandler-Wilde, S.N., Levesley, J. & Hough, D.M. Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain. Adv Comput Math 3, 115–135 (1995). https://doi.org/10.1007/BF03028363
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DOI: https://doi.org/10.1007/BF03028363