Conformal map building

Conformal map has application in a lot of areas of science, e.g., fluid flow, heat conduction, solidification, electromagnetic, etc. Especially conformal map applied to elasticity theory can provide most simple and useful solution. But finding of conformal map for custom domain is not trivial problem. We used a numerical method for building a conformal map to solve torsion problem. The main idea of the method is to build a conformal map as a polynomial of a finite degree. In this case conformity is violated in the corner points, but this problem can be prevented by replacing of piecewise smooth boundary by curve with the continuously changing tangent. In addition it was considered an infinite system method to solve the same problem. Torsion problem for the cross-shaped prism was solved by numerical conformal maps method and infinite system method. Results are compared.