Conformal Mapping Using the Schwarz-Christoffel Transform

The Schwarz-Christoffel transform is a conformal mapping from the upper half of the complex plane to a polygonal domain. It allows many physical problems posed on two-dimensional, polygonal regions, such as heat flow, fluid flow, and elec-trostatics, to be solved numerically. This type of problem cannot generally be solved in closed form; the Schwarz-Christoffel transform provides an exceptionally accurate method of solution. This paper describes the implementation of a working software unit that efficiently and accurately calcu-lates Schwarz-Christoffel transforms and inverses. The program incorporates graphical, easy-to-use interfaces and will contain resources to aid in solving physical problems. Future research into mathematical extensions to the Schwarz-Christoffel transform, such as the inclusion of simple curves, will be conducted