Singular matrices arising in the MFS from certain boundary and pseudo-boundary symmetries

We consider the application of the method of fundamental solutions (MFS) to certain two–dimensional second order boundary value problems (BVPs). We assume that the domain of the problem under consideration is a regular polygon and that the sources in the MFS are placed uniformly on a circle concentric to and surrounding the polygon. For certain uniform distributions of the collocation points we prove that, for general classes of regular polygons, the MFS discretization leads to singular coefficient matrices.