The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions

We investigate applications of the method of fundamental solutions (MFS) for the numerical solution of two-dimensional boundary value problems in complex geometries, governed by the Laplace equation and subject to Dirichlet boundary conditions which are not harmonic. Such problems can be very challenging because of the appearance of boundary singularities. We consider several ways of choosing the boundary collocation points as well as the source points in the MFS. We show that with an appropriate such choice the MFS yields highly accurate results.