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Efficient Calculation of Schwarz–Christoffel Transformations for Multiply Connected Domains Using Laurent Series

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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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Notes

  1. “No singularity may lie closer to an integration sub-interval than one-half the length of that subinterval.” [12].

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS, 67260-0033, USA

    Thomas K. DeLillo & Alan R. Elcrat

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Everett H. Kropf

  3. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    John A. Pfaltzgraff

Authors
  1. Thomas K. DeLillo
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  2. Alan R. Elcrat
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  3. Everett H. Kropf
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  4. John A. Pfaltzgraff
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Correspondence to Thomas K. DeLillo.

Additional information

Communicated by Lloyd N. Trefethen.

Dedicated to Nicolas Papamichael

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DeLillo, T.K., Elcrat, A.R., Kropf, E.H. et al. Efficient Calculation of Schwarz–Christoffel Transformations for Multiply Connected Domains Using Laurent Series. Comput. Methods Funct. Theory 13, 307–336 (2013). https://doi.org/10.1007/s40315-013-0023-1

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  • DOI: https://doi.org/10.1007/s40315-013-0023-1

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