AN EXTENDED SCHWARZCHRISTOFFEL TRANSFORMATION FOR NUMERICAL MAPPING OF POLYGONS WITH CURVED SEGMENTS

AN EXTENDED SCHWARZCHRISTOFFEL TRANSFORMATION FOR NUMERICAL MAPPING OF POLYGONS WITH CURVED SEGMENTS An extension of the SchwarzChristoffel transformation is described to formally map polygons which contain curved boundaries. The curved boundaries are divided into small curved elements and each element is approximated by a second degree polynomial higher degree polynomials can also be used. The iterative algorithm of evaluating the unknown constants of the basic SC transformation described in a companion paper is applied to the extended SC transformation to compute its unknown constants, including the coefficients of the polynomials. Excellent results are achieved as far as accuracy and convergence are concerned. Examples including a practical application, are provided. The mapping of curved polygons is important because they provide a better model of a physical device. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

AN EXTENDED SCHWARZCHRISTOFFEL TRANSFORMATION FOR NUMERICAL MAPPING OF POLYGONS WITH CURVED SEGMENTS

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0332-1649
DOI
10.1108/eb010092
Publisher site
See Article on Publisher Site

Abstract

An extension of the SchwarzChristoffel transformation is described to formally map polygons which contain curved boundaries. The curved boundaries are divided into small curved elements and each element is approximated by a second degree polynomial higher degree polynomials can also be used. The iterative algorithm of evaluating the unknown constants of the basic SC transformation described in a companion paper is applied to the extended SC transformation to compute its unknown constants, including the coefficients of the polynomials. Excellent results are achieved as far as accuracy and convergence are concerned. Examples including a practical application, are provided. The mapping of curved polygons is important because they provide a better model of a physical device.

Journal

COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Feb 1, 1992

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