Space-time discontinuous Petrov-Galerkin methods for linearwave equations in heterogeneous media

We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves in Gopalakrishnan / Sepulveda (A space-time DPG method for acoustic waves, arXiv 2017) and in Ernesti / Wieners (RICCAM proceedings, submitted 2017) and is based on the abstract definition of traces on the skeleton of the time-space sub-structuring. The method is evaluated by large-scale parallel computations motivated from applications in seismic imaging, where the computational domain can be restricted substantially to a subset of the full space-time cylinder.