Eigendecompositions and fast eigensolvers for Maxwell equations (Q679550)

This review paper reports on some results concerning the computation of the band structures of photonic crystals. The methods discussed allow to deduce explicit eigen-decompositions for the discrete single and double curl operators associated with the eigenvalue problems associated to the discretization of the Maxwell eigenvalue problem. On the one side, these eigen-decompositions can be computed by using the fast Fourier method. On the other side, it seems that the efficient computational realization of the null space enables to derive the null space free method. The results are illustrated and supported by numerical examples.