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The problem of accelerating the calculation of the periodic Green's function is addressed here for both 3-D and 2-D free-space configurations. In the 3-D case, periodicity is considered both along one axis and along two, generally skew, axes. A comprehensive review of the existing methods is first presented and some extensions are developed. The possibility of treating the case of complex phase shifts between unit cells, necessary for the study of complex modes in periodic structures, is also investigated. Comparisons among the various acceleration methods are performed, thus providing fundamental information on their actual efficiency in typical problems.