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Multiply Connected Regions

In: Computational Conformal Mapping

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  • Prem K. Kythe

    (University of New Orleans, Department of Mathematics)

Abstract

We shall discuss some existence and uniqueness theorems for the conformal mappings of multiply connected regions onto canonical regions. The numerical method presented here is based on Mikhlin’s integral equation formulation on the boundary, which is a Fredholm integral equation of the second kind and has a unique periodic solution.Then a numerical method, called Mayo’s method, that uses a fast Poisson solver for the Laplacian (Mayo 1984) is employed to determine the mapping function in the interior of the region which can be simply, doubly, or multiply connected, with accuracy even near the boundary. This method, in fact, computes the derivatives of the mapping function in the first application and the mapping function itself if applied twice.

Suggested Citation

  • Prem K. Kythe, 1998. "Multiply Connected Regions," Springer Books, in: Computational Conformal Mapping, chapter 0, pages 358-378, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2002-2_14
    DOI: 10.1007/978-1-4612-2002-2_14
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