  We expand the applicabilities and capabilities of an already existing
space-time parallel method based on a block Jacobi smoother. First we formulate
a more detailed criterion for spatial coarsening, which enables the method to
deal with unstructured meshes and varying material parameters. Further we
investigate the application to the eddy-current equation, where the non-trivial
kernel of the curl operator causes severe problems. This is remedied with a new
nodal auxiliary space correction. We proceed to identify convergence rates by
local Fourier analysis and numerical experiments. Finally, we present a
numerical experiment which demonstrates its excellent scaling properties.
