Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain
type: Item
instance of: scholarly article
title: Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain
zbMATH Open document ID: 0834.30008
DOI: 10.1007/BF03028363
author: David M. Hough
author: Simon N. Chandler-Wilde
author: Jeremy Levesley
published in: Advances in Computational Mathematics
publication date: 1995-10-09T00:00:00Z
review text: The conformal mapping \(g\) of the interior or exterior of the unit circle onto a simply-connected domain \(\Omega\) with corners is represented as a boundary integral containing \(f|_{\partial\Omega}\). Hereby, the inverse mapping \(f:= g^{- 1}\), which can be obtained e.g. as solution of Symm's integral equation, is considered as known on the boundary \(\partial\Omega\). Due to the corners of \(\Omega\) the representation for \(g\) contains integrals over the product of weakly singular functions and is ill- conditioning near the corner points. This leads to significant numerical problems. The authors describe and analyse quadrature schemes appropriate for these difficulties based on product integration. The efficacy of this method is illustrated with numerical experiments.
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 803466
zbMATH Keywords: corner singularities
zbMATH Keywords: conformal mapping
zbMATH Keywords: boundary integral
zbMATH Keywords: Symm's integral equation
zbMATH Keywords: weakly singular functions
zbMATH Keywords: quadrature schemes
zbMATH Keywords: product integration
zbMATH Keywords: numerical experiments
reviewed by: Andreas Pomp
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03028363
OpenAlex ID: W1992768729
description: scientific article; zbMATH DE number 803466