A Mixed Basis Perturbation Approach to Approximate the Spectrum of Laplace Operator

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.