Parallel Adaptive Space-Time Methods for Parabolic Evolution Problems
In this talk, we consider all-at-once space-time methods for quasi-linear parabolic evolution equations. In particular, we will focus on goal-oriented adaptivity driven by the dual-weighted residual (DWR) method, where we also permit mulitple and possibly non-linear goal functionals. Moreover, we evaluate the parallel performance of the adaptive method. Since we use an all-at-once discretization approach, the parallelization of the solver for the possibly non-linear systems of equations is straightforward. We discuss the localization via the partition-of-unity method for distributed memory parallelization. Finally, we present various numerical experiments that demonstrate the performance of the parallel goal-oriented space-time finite element solver for different kinds of functionals.
