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A three-dimensional finite-element method with efficient boundary conditions is presented to simulate the electromagnetic properties of heterogeneous periodic materials. The analysis based on a waveguide approach applies to arbitrary profiles with any kind of inclusions for all incidence conditions. Floquet's theorem is used to take into account the periodicity of the problem. This method allows one to handle the scattering effects in the material. For periodically organized composite materials, we can extract an effective permeability and permittivity under certain hypotheses.