Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series
DeLillo, Thomas K.
Elcrat, Alan R.
Pfaltzgraff, J. A.
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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
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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