NUMERICAL COMPUTATION OF THE SCHWARZ‐CHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING OF ARBITRARILY SHAPED POLYGONS WITH FINITE VERTICES

Abstract

An iterative algorithm is described to compute Schwarz‐Christoffel 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 S‐C 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 S‐C transformation are in the solution of Laplace's and Poisson's equation in two‐dimensional domains with polygonal boundary.

Citation

CHAUDHRY, M.A. and SCHINZINGER, R. (1992), "NUMERICAL COMPUTATION OF THE SCHWARZ‐CHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING OF ARBITRARILY SHAPED POLYGONS WITH FINITE VERTICES", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 11 No. 2, pp. 263-275. https://doi.org/10.1108/eb010091