# Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains

@article{Vasconcelos2014GeneralizationOT, title={Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains}, author={Giovani L. Vasconcelos}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2014}, volume={470} }

A generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function…

## 3 Citations

### Periodic Schwarz–Christoffel mappings with multiple boundaries per period

- MathematicsProceedings of the Royal Society A
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We present an extension to the theory of Schwarz–Christoffel (S–C) mappings by permitting the target domain to be a single period window of a periodic configuration having multiple polygonal…

### Secondary Schottky–Klein prime functions associated with multiply connected planar domains

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

In recent years, a general mathematical framework for solving applied problems in multiply connected domains has been developed based on use of the Schottky–Klein (S–K) prime function of an…

### Multiple steadily translating bubbles in a Hele-Shaw channel

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles.

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Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles.

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The SC toolbox can be used as a starting point for many different types of computing, and the toolbox itself can be modified to suit the needs of the learner.