Convergence of Parareal with spatial coarsening

Daniel Ruprecht (Hamburg University of Technology)

When solving PDEs, using a coarser spatial mesh in Parareal’s coarse propagator can be an effective way to reduce its cost and improve potential speedup. However, the cost reduction has to be balanced against potentially slower convergence. In the talk, we will prove a theoretical best-case bound for the norm of Parareal’s iteration matrix when spatial coarsening is used. We will discuss implications of the result and compare it to numerical experiments. One consequence of the bound is that for hyperbolic problems, where Parareal is known to struggle, spatial coarsening will eliminate any chance for a theoretical guarantee of fast convergence.