On the fast multipole method for periodic and non-periodic boundary value problems in periodic domains

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Wave problems in periodic structures constitute an interesting academic area of research which has applications such as photonic crystals and metamaterials in optics and phononic crystals in elastodynamics. We have developed the periodic fast multipole method (FMM) as a fast solver of wave problems in periodic structures. But, this method still has a few restrictions which have to be removed. In this research we have extended the applicability of the periodic FMM in acoustics, elastodynamics and electromagnetics. Specifically, we have developed methods for analysing responses of periodic structures subject to non-periodic incident waves or waves in slightly perturbed periodic structures.