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- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-016-0159-x
- Publisher site
- See Article on Publisher Site
Abstract
We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For $$\ell $$ ℓ -times connected domains, the method requires solving $$\ell $$ ℓ boundary integral equations with the Neumann kernel. This can be done in $$O(\ell ^2 n \log n)$$ 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.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Feb 2, 2016