# An investigation of challenges for a time-parallel method

## Martin Schwalsberger

**Jan. 9, 2018, 2:30 p.m. S2 416-1**

In the upcoming presentation we will investigate challenges for the timeparallel-multigrid method introduced by Martin NeumÃ¼ller. 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.