Efficiency of parallel in time methods for coupled PDEs on moving domains

In recent years, several parallel in time methods have been developed. Amongst them are ParaReal, ParaExp and PFASST. In this talk, we apply these methods to the heat conduction problem of a coupled machine tool, which consists of several parts and materials. Neighboring parts are coupled at their common boundary with a robin type boundary condition. The challenging part comes from the fact that parts may move with respect to each other. We discretize the coupled PDE system on varying domains in space by finite elements. Due to the movement, we obtain a multi scale ODE containing the time scale of diffusion and the time scale of the movement. We apply different parallel in time methods on the resulting multi scale ODE and compare their parallel efficiency in numerical experiments.