General conformal transformation method based on Schwarz-Christoffel approach

Note on the Inversion of the Schwarz-Christoffel Conformal Transformation

An inversion procedure, based on the methods used in proving Btirmasm’s theorem, is used to provide an integral expression which exhibits the form of the electrostatic field explicitly in terms of the field coordinates. The method is illustrated with an example of a stepped-guide junction. The form of the field and the expression for the mode expansion coefficients are examined. The results are...

A Modified Schwarz-christoffel Transformation for Elongated

The numerical computation of a conformal map from a disk or a half plane onto an elongated region is frequently difficult, or impossible, because of the so-called crowding phenomenon. This paper shows that this problem can often be avoided by using another elongated region, an infinite strip, as the standard domain. A transformation similar to the Schwarz-Christoffel formula maps this strip ont...

A Generalization of the Schwarz-Christoffel Transformation.

The classical Schwarz-Christoffel transformation provides a formula for the conformal mapping of the half-plane onto a plane polygon. A generalization enlarging the class of image domains to include many-sheeted plane polygons with interior winding points was known already to at least Schwarz and Schlifli.' This note is concerned with a further simple extension of the formula which delivers a u...

A Software Package for Computing Schwarz-Christoffel Conformal Transformation for Doubly Connected Polygonal Regions

A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this paper from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is ...

Separation - of - Variables Solution from the Schwarz - Christoffel Transformation