Collocation approach to the Helmholtz eigenvalue problem on multiply connected domains

We present a collocation approach to the numerical solution of the Helmholtz eigenvalue problem on multiply connected domains of arbitrary shape in two dimensions. A suitable representation of the Helmholtz equation on an uniform grid is obtained and the problem is converted to the calculation of the first few eigenvalues and eigenvectors of a large sparse matrix. The accuracy of this approach is tested by performing a comparison with results available in the literature. The flexibility and simplicity of the method make easy the application to arbitrary geometries.