An investigation of challenges for a time-parallel method

Martin Schwalsberger

Jan. 9, 2018, 3:30 p.m. S2 416-1

In the upcoming presentation we will investigate challenges for the timeparallel-
multigrid method introduced by Martin Neumuller. We will mainly
focus on problems related to the so called "space-coarsening-strategy". When
calculating a coarse time-grid correction, it decides whether or not also a
coarser spatial mesh may be used. This allows to speed up less parallel sections
of the algorithm.
For the case of the heat-equation with constant coefficients the existing
analysis guarantees optimal behavior by following a simple rule. We
present numerical experiments for the case of jumping coefficients and for
the case of the Eddy-current equation. For jumping coefficients the spacecoarsening
strategy must be generalized and verified. Unfortunately the
infinite-dimensional kernel of the curl operator is suspected to introduce
severe problems for the current approach, which needs to be resolved.
Finally we conclude the talk with performance experiments for the current
version of the developed program.