The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains

In this paper a new boundary method for Helmholtz eigenproblems in simply and multiply connected domains is presented. The method is based on mathematically modelling the physical response of a system to external excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. So, contrary to the traditional scheme, the method described does not involve evaluation of determinants of linear systems. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. The method shows a high precision in simply and multiply connected domains. The results of the numerical experiments justifying the method are presented.