In this work we present a numerical algorithm for the determination of the eigenvalues and eigenfunctions associated to the Dirichlet problem for the Laplacian, in a bounded or in an exterior domain. The determination of higher eigenfrequencies is a well-known numerical problem, that has been addressed with other numerical methods. Here we propose to use the method of fundamental solutions. Since the MFS produces highly ill conditioned matrices, a particular technique was derived to overcome the difficulty of determining accurately those eigenfrequencies. Extensive numerical simulations will be presented.

CEMAT - Center for Computational and Stochastic Mathematics