On the Schwarz-Christoffel transformation and $p$-valent functions

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...

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...

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

Two-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...