Rigorous convergence proof of space-time multigrid with coarsening in space (Q2066221)

The author presents a full convergence proof of space-time multigrid with coarsening in space, considering two families of smoothers that are well adapted to parallel computation. For waveform type smoothers, it is proved that the convergence can be uniform with respect to both the time step size and the mesh size. Such convergence result is not straightforward. It is also shown that time-parallel smoothers perform as well as waveform type smoother as long as the ratio \(\eta\) between the square mesh size and the time step size is below some threshold. Some numerical tests are presented to show the accuracy of the theoretical estimates.