A method is given for solving two dimensional
harmonic mixed boundary value problems in simply-connected polygonal domains with re-entrant boundaries. The method consists of a numerical conformal mapping together with three other conformal transformations. The numerical mapping transforms the original domain onto the unit circle,
which in turn is mapped onto a rectangle by means of two bilinear and one Schwarz-Christoffel transformations. The transformed problem in the rectangle is solved by inspection
