The Application of Numerical Methods to the Conformal Transformation of Polygonal Boundaries

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Abstract
This paper describes a highly efficient numerical method for evaluating the constants of the Schwarz-Christoffel transformation equation of complex polygonal boundaries. It uses a combination of a direct search simplex technique to minimize the sum of squares of the errors in the dimensions of the polygon and Gauss-Jacobi Quadrature formulae to evaluate the elements of the error function. The performance of the method as applied to a typical electrical engineering problem is discussed.

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