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NUMERICAL COMPUTATION OF THE SCHWARZCHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING OF ARBITRARILY SHAPED POLYGONS WITH FINITE VERTICES

NUMERICAL COMPUTATION OF THE SCHWARZCHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING... An iterative algorithm is described to compute SchwarzChristoffel transformations which map the upper half of a complex plane into the interior of a polygon in another complex plane. An efficient method of numerically integrating the SC integral over the singularities is presented. The algorithm is easily programmable in FORTRAN. Convergence rate is high and accuracy is excellent. Examples are provided and wherever possible, analytically obtained results are also presented for comparison. The importance of the algorithm is described and a brief comparison with some of the existing algorithms is made. Potential application of the SC transformation are in the solution of Laplace's and Poisson's equation in twodimensional domains with polygonal boundary. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

NUMERICAL COMPUTATION OF THE SCHWARZCHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING OF ARBITRARILY SHAPED POLYGONS WITH FINITE VERTICES

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0332-1649
DOI
10.1108/eb010091
Publisher site
See Article on Publisher Site

Abstract

An iterative algorithm is described to compute SchwarzChristoffel transformations which map the upper half of a complex plane into the interior of a polygon in another complex plane. An efficient method of numerically integrating the SC integral over the singularities is presented. The algorithm is easily programmable in FORTRAN. Convergence rate is high and accuracy is excellent. Examples are provided and wherever possible, analytically obtained results are also presented for comparison. The importance of the algorithm is described and a brief comparison with some of the existing algorithms is made. Potential application of the SC transformation are in the solution of Laplace's and Poisson's equation in twodimensional domains with polygonal boundary.

Journal

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

Published: Feb 1, 1992

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