Computational Conformal Mapping in Education and Engineering Practice

Abstract

Conformal mapping techniques can help engineers with their tasks of analysis and design applied to a wide range of applications, including structural members, electric and magnetic fields, microcircuits, heat flow, and fluid flow. Conformal mapping of potential fields associated with a wide range of configurations provides not only numerical results but also yields answers in analytical form that provide insight and the opportunity to make intelligent decisions regarding suitable modification of field boundaries in their ultimate physical manifestations. Conformal mapping provides answers that are not only of value to practicing engineers but also to students who will benefit from a more thorough understanding of potential field concepts in a wide range of engineering disciplines. First part of this paper describes the use of the Schwarz-Christoffel transformation which can be applied successfully to a wide range of polygonal configurations of arbitrary shapes. A simple numerical algorithm is described to compute the shape-specific constants of the mapping function. Second part of the paper describes some common mapping functions that can be used to demonstrate concepts of field theory and conformal mapping to undergraduate students of science and engineering.