Geodesic
Numerical Conformal Mappings of Unbounded Multiply-Connected Domains Using the Charge Simulation Method
Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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We present a numerical method of conformal mappings of unbounded multiply-connected domains exterior to closed Jordan curves onto the three types of canonical domains of Nehari, i.e., the parallel slit domain, the circular slit domain and the radial slit domain. In the method, we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method is simple without integration and suited for domains with curved boundaries. In particular, approximate mapping functions of an unbounded multiply-connected domain onto the three types of slit domains are obtained in a unified way by solving linear equations with a common coefficient matrix. A typical example shows the effectiveness of the method. 
@article{BMMS_2003_26_1_a4,
     author = {Kaname Amano, Dai Okano and Hidenori Ogata and Masaaki Sugihara},
     title = {Numerical
                        {Conformal} {Mappings} of {Unbounded} {Multiply-Connected} {Domains
}                        {Using} the {Charge} {Simulation} {Method}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2003},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a4/}
}
TY  - JOUR
AU  - Kaname Amano, Dai Okano
AU  - Hidenori Ogata
AU  - Masaaki Sugihara
TI  - Numerical
                        Conformal Mappings of Unbounded Multiply-Connected Domains
                        Using the Charge Simulation Method
JO  - Bulletin of the Malaysian Mathematical Society
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VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a4/
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%0 Journal Article
%A Kaname Amano, Dai Okano
%A Hidenori Ogata
%A Masaaki Sugihara
%T Numerical
                        Conformal Mappings of Unbounded Multiply-Connected Domains
                        Using the Charge Simulation Method
%J Bulletin of the Malaysian Mathematical Society
%D 2003
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a4/
%F BMMS_2003_26_1_a4
Kaname Amano, Dai Okano; Hidenori Ogata; Masaaki Sugihara. Numerical
                        Conformal Mappings of Unbounded Multiply-Connected Domains
                        Using the Charge Simulation Method. Bulletin of the Malaysian Mathematical Society, Tome 26 (2003) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2003_26_1_a4/