Numerical solution of eigenproblems in PDEs using the Method of Fundamental Solutions

In this talk we consider the application of the Method of Fundamental Solutions (MFS) to calculate eigenvalues and eigenfunctions of the Laplacian (2D and 3D domains). We show that a particular choice of the point-sources allows to obtain very good results for a fairly general class of domains. The case of regions with corners and cracks is also addressed enriching the MFS basis of functions with some particular solutions adapted to these domains. We also present results of the application of the MFS to the eigenvalue problem associated to the Bilaplacian operator and to the Lamé operator, in the elastic case.