Numerical Computation of the Conformal Map onto Lemniscatic Domains

We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For ℓ -times connected domains, the method requires solving ℓ boundary integral equations with the Neumann kernel. This can be done in O ( ℓ 2 n log n ) operatio...

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Bibliographic Details
Published in:Computational methods and function theory 2016-12, Vol.16 (4), p.609-635
Main Authors: Nasser, Mohamed M. S., Liesen, Jörg, Sète, Olivier
Format: Article
Language:English
Subjects:
Analysis
Boundaries
Boundary integral method
Computation
Computational Mathematics and Numerical Analysis
Conformal mapping
Functions of a Complex Variable
Integral equations
Mathematics
Mathematics and Statistics
Numerical analysis
Smooth boundaries
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Summary:We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For ℓ -times connected domains, the method requires solving ℓ boundary integral equations with the Neumann kernel. This can be done in O ( ℓ 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.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-016-0159-x