  We propose and investigate new robust preconditioners for space-time
Isogeometric Analysis of parabolic evolution problems. These preconditioners
are based on a time parallel multigrid method. We consider a decomposition of
the space-time cylinder into time-slabs which are coupled via a discontinuous
Galerkin technique. The time-slabs provide the structure for the time-parallel
multigrid solver. The most important part of the multigrid method is the
smoother. We utilize the special structure of the involved operator to decouple
its application into several spatial problems by means of generalized
eigenvalue or Schur decompositions. Some of these problems have a symmetric
saddle point structure, for which we present robust preconditions. Finally, we
present numerical experiments confirming the robustness of our space-time IgA
solver.
