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Numerical conformal mappings onto the linear slit domain

  • Kaname Amano
  • Dai Okano
  • Hidenori Ogata
  • Masaaki Sugihara
Open Access
Original Paper Area 1

Abstract

We propose a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves C 1, . . . ,C n onto a canonical linear slit domain, which is the entire plane with linear slits S 1, . . . , S n of angles θ 1, . . . , θ n arbitrarily assigned to the real axis, respectively. If θ 1 = · · · = θ n θ then it is the well-known parallel slit domain, which is important in the problem of potential flows past obstacles. In the method, we reduce the mapping problem to a boundary value problem for an analytic function, and approximate it by a linear combination of complex logarithmic functions based on the charge simulation method. Numerical examples show the effectiveness of our method.

Keywords

Conformal mapping Multiply connected domain Potential flow Charge simulation Fundamental solution 

Mathematics Subject Classification

30C30 65E05 

Notes

Acknowledgments

The authors wish to thank Emeritus Prof. M. Shiba (Hiroshima University) and Prof. T. Sakajo (Hokkaido University) for their helpful discussion.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Kaname Amano
    • 1
  • Dai Okano
    • 1
  • Hidenori Ogata
    • 2
  • Masaaki Sugihara
    • 3
  1. 1.Department of Electrical and Electronic Engineering and Computer Science, Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan
  2. 2.Department of Communication Engineering and Informatics, Graduate School of Informatics and EngineeringThe University of Electro-CommunicationsChofuJapan
  3. 3.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan

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