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arXiv · 1505.04916

Numerical computation of the conformal map onto lemniscatic domains

Mohamed M. S. Nasser·Jörg Liesen·Olivier Sète
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Abstract

We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For $\ell$-times connected domains the method requires solving $\ell$ boundary integral equations with the Neumann kernel. This can be done in $O(\ell^2 n \log n)$ operations, where $n$ is the number of nodes in the discretization of each boundary component of the multiply connected domain. As demonstrated by numerical examples, the method works for domains with close-to-touching boundaries, non-convex boundaries, piecewise smooth boundaries, and for domains of high connectivity.

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Mohamed M. S. Nasser, Jörg Liesen, Olivier Sète. 2015-12-15. Numerical computation of the conformal map onto lemniscatic domains. https://doi.org/10.1007/s40315-016-0159-x

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