Numerical conformal mapping based on the generalised conjugation operator |
| |
| Authors: | Bao Cheng Li Stavros Syngellakis. |
| |
| Affiliation: | Computervision R&D, 138-144 London Road, Wheatley, Oxon OX33 1JH, United Kingdom ; Department of Mechanical Engineering, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom |
| |
| 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. |
| |
| Keywords: | Numerical conformal mapping conjugation operator boundary integral equation |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
|
点击此处可从《Mathematics of Computation》下载全文 |
