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Numerical Computing of Preimage Domains for Bounded Multiply Connected Slit Domains

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Abstract

In this paper, for a given bounded multiply connected slit domain \(\varOmega \), we present an iterative numerical method for computing a conformally equivalent multiply connected domain G bounded by smooth Jordan curves and the conformal mapping \(w=\varPhi (z)\) from G onto \(\varOmega \). Each iteration of the proposed iterative method requires solving the boundary integral equation with the generalized Neumann kernel. We consider two cases of bounded slit domains, namely the unit disk with radial slit domain and an annulus with radial slit domain. Numerical examples are presented to illustrate that the proposed iterative method converges even for highly connected slit domains.

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Acknowledgements

The author is grateful to an anonymous referee for his valuable comments and suggestions which improved the results and the presentation of this paper. Further, the author thanks Prof. Leslie Greengard and Dr. Zydrunas Gimbutas for making the MATLAB toolbox FMMLIB2D [17] publicly available.

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  1. Department of Mathematics, Statistics and Physics, Qatar University, P.O.Box 2713, Doha, Qatar

    Mohamed M. S. Nasser

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Nasser, M.M.S. Numerical Computing of Preimage Domains for Bounded Multiply Connected Slit Domains. J Sci Comput 78, 582–606 (2019). https://doi.org/10.1007/s10915-018-0784-9

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