Multiply Connected Regions

Prem K. Kythe
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Prem K. Kythe: University of New Orleans, Department of Mathematics

Chapter Chapter 13 in Computational Conformal Mapping, 1998, pp 358-378 from Springer

Abstract: 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.

Keywords: Unit Disk; Dirichlet Problem; Mapping Function; Conformal Mapping; Mesh Point (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2002-2_14

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DOI: 10.1007/978-1-4612-2002-2_14

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