  We present a finite-element simulation tool for calculating light fields in
3D nano-optical devices. This allows to solve challenging problems on a
standard personal computer. We present solutions to eigenvalue problems, like
Bloch-type eigenvalues in photonic crystals and photonic crystal waveguides,
and to scattering problems, like the transmission through finite photonic
crystals.
  The discretization is based on unstructured tetrahedral grids with an
adaptive grid refinement controlled and steered by an error-estimator. As
ansatz functions we use higher order, vectorial elements (Nedelec, edge
elements). For a fast convergence of the solution we make use of advanced
multi-grid algorithms adapted for the vectorial Maxwell's equations.
