Prof. Dr. Christian Wieners (Karlsruhe Institute of Technology)
Parallel space-time methods for linear hyperbolic systems
(Monday, 02.03.20, 13:30-14:25, lecture hall H12)
We consider variational space-time discretizations of linear first-order hyperbolic systems. Based on the theory for symmetric Friedrichs systems we establish an analytic framework and we prove inf-sup stability of the continuous variational setting.
Discrete inf-sup stability is obtained for a space-time method with discontinuous Galerkin elements with upwind flux in space and weakly continuous Galerkin elements in time. The discretization is adaptive with independent choice of polynomial degrees $p$ in time and $q$ in space for every space-time cell. The discretization is fully implicit, and the overall linear problem is solved with a parallel Krylov method
using a multigrid preconditioner based on a subspace hierarchy. The adaptivity is controlled by a dual weighted residual error estimator with respect to a given linear error functional.
The method is evaluated for a benchmark configuration in geophysics, the full waveform inversion to identify the subsurface material distribution by seismograms. Here we consider $p$-adaptive approximations of the forward problem based on a dual-primal error estimator with respect to a goal functional corresponding to the seismic measurements.
(This talk is on joint work with W. Dörfler, J. Ernesti, S. Findeisen, and D. Ziegler)