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

Abstract

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 reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping "difficult" regions (to be specified in Section 2), and being user-friendly. Several examples are presented to demonstrate the capabilities of the package. Categories and Subject Descriptors: G.1.m [Numerical Analysis]: Miscellaneous; G.4 [Mathematics of Computing]: Mathematical Software-efficiency, reliability, and robustness General Terms: Algorithms Additional Key Words and Phrases: Numerical Conformal Mapping, Schwarz-Christoffel conformal transformation, doubly connected region, accessory parameters, system of nonlinear equations 2 This work was partially supported by NSF grant OSR-9255223 under the NSF EPSCOR Program when the author was working on his dissertation at Wichita State University. The paper as well as the major revision of the package were done at Fort Hays State University where the author is currently on its faculty. 1. INTRODUCTIO