A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet boundary conditions on arbitrary triangular domains is presented. Its reliability is tested by comparing numerical results with analytical ones whenever possible. The computation of eigenvalues shows a good agreement with analytical results. The procedure is shown to give accurate results also in the case of eigenfunctions computation. Finally, the sensitivity of our scheme to the geometry of the domain is discussed and the algorithm is shown to detect small changes in the shape of the domain.
