Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series
DeLillo, Thomas K. Elcrat, Alan R. Kropf, Everett Pfaltzgraff, J. A.
DeLillo, Thomas K.
Elcrat, Alan R.
Kropf, Everett
Pfaltzgraff, J. A.
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2013-08
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Article
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Schwarz–Christoffel transformation,Conformal mapping,Multiply connected domains,Laurent series
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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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Heldermann Verlag
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Computational Methods and Function Theory;v.13:no.2
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1617-9447
2195-3724
2195-3724