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Numerical conformal mapping based on the generalised conjugation operation

Numerical conformal mapping based on the generalised conjugation operation
Numerical conformal mapping based on the generalised conjugation operation
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.
0025-5718
619-639
Li, Bao Cheng
9c6c87e2-9737-484f-9152-d93066690dce
Syngellakis, Stavros
8419e8bc-515e-49f4-8cb3-79fbcc245f5d
Li, Bao Cheng
9c6c87e2-9737-484f-9152-d93066690dce
Syngellakis, Stavros
8419e8bc-515e-49f4-8cb3-79fbcc245f5d

Li, Bao Cheng and Syngellakis, Stavros (1998) Numerical conformal mapping based on the generalised conjugation operation. Mathematics of Computation, 67 (222), 619-639.

Record type: Article

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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Published date: 1998

Identifiers

Local EPrints ID: 21180
URI: http://eprints.soton.ac.uk/id/eprint/21180
ISSN: 0025-5718
PURE UUID: a9db1a18-9b72-497f-a246-d12bf960e2aa

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Date deposited: 08 Nov 2006
Last modified: 22 Jul 2020 16:39

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Contributors

Author: Bao Cheng Li
Author: Stavros Syngellakis

University divisions

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