Conformal transformation employing direct-search techniques of minimisation

The paper deals with the transformation by numerical techniques of fields having polygonal boundaries. Modern direct-search techniques for the minimisation of multivariable functions are employed, together with a method of integration in which the step length is continuously and automatically varied. The complete solution procedure is highly efficient; it converges smoothly for all boundary shapes studied and has the important feature for general application that it is virtually independent of experience on the part of the analyst. A discussion of typical functional variations and a transformation simplifying the integration of functions with complex limits are included. An example is considered to show the application of the method, and guidance is given on the performance to be expected in the general application of the method.