Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series

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Authors
DeLillo, Thomas K.
Elcrat, Alan R.
Kropf, Everett
Pfaltzgraff, J. A.
Advisors
Issue Date
2013-08
Type
Article
Keywords
Schwarz–Christoffel transformation , Conformal mapping , Multiply connected domains , Laurent series
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Citation
DeLillo, Thomas K.; Elcrat, Alan R.; Kropf, Everett; Pfaltzgraff, J.A. 2013. Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series. Computational Methods and Function Theory, August 2013, v.13:no.2:pp 307-336
Abstract

We discuss recently developed numerics for the Schwarz–Christoffel transformation for unbounded multiply connected domains. The original infinite product representation for the derivative of the mapping function is replaced by a finite factorization where the inner factors satisfy certain boundary conditions derived here. Least squares approximations based on Laurent series are used to satisfy the boundary conditions. This results in a much more efficient method than the original method based on reflections making the accurate mapping of domains of higher connectivity feasible.

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Publisher
Heldermann Verlag
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Series
Computational Methods and Function Theory;v.13:no.2
PubMed ID
DOI
ISSN
1617-9447
2195-3724
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