Improvements in numerical techniques for conformal transformation with particular reference to electromagnetic fields

Some significant improvements achieved in numerical methods for conformal transformation applicable to electromagnetic field analysis are reported. It is shown that the basic Schwarz-Christoffel equation, which at each of the vertices always results in either a pole or a zero, can be accurately and efficiently integrated by employing a combination of quadrature methods and simple variable transformations. Other transformations are also described to constrain the -plane constants as required during the direct-search minimization. The complete procedure developed applies to almost any geometry and is found to be computationally faster and more reliable than previous methods. The procedure is illustrated with the aid of an electrical-machine example specifically to which pertain the numerical results and some of the equations.