In this paper, different formulations of Maxwell equations are combined for computing the shielding effectiveness of enclosures made from heterogeneous periodic materials. The validity of the homogenized parameters given by Maxwell-Garnett rules in the frequency domain are tested in the time domain by using a nodal DG method, which uses an interface condition based on analytical solution in the frequency domain to replace a conductive sheet. This interface condition allows to avoid meshing the thin sheet, thus reducing the computational cost. Results of scattering by composite enclosures are presented in the frequency domain thanks to a FFT.