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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Numerical conformal mapping based on the generalised conjugation operator
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by Bao Cheng Li and Stavros Syngellakis PDF
Math. Comp. 67 (1998), 619-639 Request permission

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
  • Email: baoli@cvedg.cv.com
  • Stavros Syngellakis
  • Affiliation: Department of Mechanical Engineering, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
  • Email: ss@soton.ac.uk
  • Received by editor(s): September 7, 1995
  • Received by editor(s) in revised form: September 19, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 619-639
  • MSC (1991): Primary 30C30; Secondary 65N38
  • DOI: https://doi.org/10.1090/S0025-5718-98-00957-0
  • MathSciNet review: 1464146