  We present robust and highly parallel multilevel non-overlapping Schwarz
preconditioners, to solve an interior penalty discontinuous Galerkin finite
element discretization of a system of steady state, singularly perturbed
reaction-diffusion equations with a singular reaction operator, using a GMRES
solver. We provide proofs of convergence for the two-level setting and the
multigrid V-cycle as well as numerical results for a wide range of regimes.
