Static Green's functions with conformal mapping and MATLAB

In this paper, conformal mapping was combined with Matlab. An application of the theory was showed in examples showing its ability to provide analytical expressions for two-dimensional Green's functions associated with Poisson's equation, i.e., electrostatic potentials created by infinite line sources parallel to metallic infinite cylinders of the various shapes. The solution is naturally expressed in the transformed domain, but usually a direct expression in the original (x,y) coordinates is easily obtained. In most cases, the proposed solutions are an order of magnitude simpler than those obtained by other approaches.