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Numerical conformal mapping based on the generalised conjugation operator

Authors: Bao Cheng Li and Stavros Syngellakis
Journal: Math. Comp. 67 (1998), 619-639
MSC (1991): Primary 30C30; Secondary 65N38
MathSciNet review: 1464146
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Abstract: An iterative procedure for numerical conformal mapping is presented which imposes no restriction on the boundary complexity. The formulation involves two analytically equivalent boundary integral equations established by applying the conjugation operator to the real and the imaginary parts of an analytical function. The conventional approach is to use only one and ignore the other equation. However, the discrete version of the operator using the boundary element method (BEM) leads to two non-equivalent sets of linear equations forming an over-determined system. The generalised conjugation operator is introduced so that both sets of equations can be utilised and their least-square solution determined without any additional computational cost, a strategy largely responsible for the stability and efficiency of the proposed method. Numerical tests on various samples including problems with cracked domains suggest global convergence, although this cannot be proved theoretically. The computational efficiency appears significantly higher than that reported earlier by other investigators.

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Additional Information

Bao Cheng Li
Affiliation: Computervision R&D, 138-144 London Road, Wheatley, Oxon OX33 1JH, United Kingdom

Stavros Syngellakis
Affiliation: Department of Mechanical Engineering, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom

Keywords: Numerical conformal mapping, conjugation operator, boundary integral equation
Received by editor(s): September 7, 1995
Received by editor(s) in revised form: September 19, 1996
Article copyright: © Copyright 1998 American Mathematical Society