  This paper presents a mixed basis approach for Laplace eigenvalue problems,
which treats the boundary as a perturbation of the free Laplace operator. The
method separates the boundary from the volume via a generic function that can
be pre-calculated and thereby effectively reduces the complexity of the problem
to a calculation over the surface. Several eigenvalues are retrieved
simultaneously. The method is applied to several 2 dimensional geometries with
Neumann boundary conditions.
