Space-time methods and fast solvers

Dr. Martin Neumüller

Oct. 15, 2013, 3:30 p.m. S2 059

For evolution equations we present a space-time method based on Discontinuous
Galerkin finite elements. Space-time methods have advantages when we have to
deal with moving domains and if we need to do local refinement in the space-time
domain. For this method we present a multigrid approach based on space-time
slaps. This method allows the use of parallel solution algorithms. In particular it
is possible to solve parallel in time and space. Numerical examples will be given
which show the performance of this space–time multigrid approach.
Moreover, an all in once multigrid method for some optimal control problems will
be presented. The main ideas of this solver are related to the presented space-time
multigrid approach. First numerical examples show the robustness of this multigrid
method.