An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D

This paper presents an FMM (fast multipole method) for periodic boundary value problems for Helmholtz' equation in 2D. The periodic Green function is an important ingredient in our formulation, which is computed efficiently with the help of the Fourier analysis. We validate the proposed method by comparing the obtained numerical results with those computed with the conventional approach. We then apply the proposed method to the analysis of scattering problems for periodic array of cracks and plot the energy transmittance vs wave numbers. The stopband and related phenomena are observed clearly. Copyright © 2007 John Wiley & Sons, Ltd.