  We consider two parallel-in-time approaches applied to a (reaction) diffusion
problem, possibly non-linear. In particular, we consider PFASST (Parallel Full
Approximation Scheme in Space and Time) and space-time multilevel strategies.
For both approaches, we start from an integral formulation of the continuous
time-dependent problem. Then, a collocation form for PFASST and a discontinuous
Galerkin discretization in time for the space-time multigrid are employed,
resulting in the same discrete solution at the time nodes. Strong and weak
scaling of both multilevel strategies is compared for varying order of the
temporal discretization. Moreover, we investigate the respective convergence
behavior for non-linear problems and highlight quantitative differences.
