Numerical conformal mappings onto the linear slit domain

被引：0
作者：
Kaname Amano
Dai Okano
Hidenori Ogata
Masaaki Sugihara
机构：
[1] Ehime University,Department of Electrical and Electronic Engineering and Computer Science, Graduate School of Science and Engineering
[2] The University of Electro-Communications,Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering
[3] The University of Tokyo,Department of Mathematical Informatics, Graduate School of Information Science and Technology
来源：
Japan Journal of Industrial and Applied Mathematics | 2012年 / 29卷
关键词：
Conformal mapping; Multiply connected domain; Potential flow; Charge simulation; Fundamental solution; 30C30; 65E05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We propose a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves C1, . . . ,Cn onto a canonical linear slit domain, which is the entire plane with linear slits S1, . . . , Sn of angles θ1, . . . , θn arbitrarily assigned to the real axis, respectively. If θ1 = · · · = θn = 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.
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页码：165 / 186
页数：21
相关论文
共 86 条
  • [1] Amano K.(1987)Numerical conformal mapping based on the charge simulation method (in Japanese) Trans. Inform. Process. Soc. Japan 28 697-704
  • [2] Amano K.(1994)A charge simulation method for the numerical conformal mapping of interior, exterior and doubly-connected domains J. Comput. Appl. Math. 53 353-370
  • [3] Amano K.(1998)A charge simulation method for numerical conformal mapping onto circular and radial slit domains SIAM J. Sci. Comput. 19 1169-1187
  • [4] Amano K.(2001)A systematic scheme of numerical conformal mappings of unbounded multiply-connected domains by the charge simulation method (in Japanese) IPSJ J. 42 385-395
  • [5] Okano D.(2009)Numerical conformal mappings onto a rectilinear slit domain by the charge simulation method (in Japanese) IPSJ J. 50 1775-1779
  • [6] Ogata H.(2010)A circular and radial slit mapping of unbounded multiply connected domains JSIAM Lett. 2 53-56
  • [7] Shimohira H.(2007)A simplified Fornberg-like method for the conformal mapping of multiply connected regions—comparisons and crowding J. Comput. Appl. Math. 209 1-21
  • [8] Sugihara M.(2006)Analytical solutions for uniform potential flow past multiple cylinders Eur. J. Mech. B Fluids 25 459-470
  • [9] Amano K.(2006)Conformal mappings between canonical multiply connected domains Comput. Methods Funct. Theory 6 59-76
  • [10] Ootori H.(1999)Numerical conformal mapping of multiply connected regions by Fornberg-like methods Numer. Math. 83 205-230
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