  We present a communication- and data-sensitive formulation of ADER-DG for
hyperbolic differential equation systems. Sensitive here has multiple flavours:
First, the formulation reduces the persistent memory footprint. This reduces
pressure on the memory subsystem. Second, the formulation realises the
underlying predictor-corrector scheme with single-touch semantics, i.e., each
degree of freedom is read on average only once per time step from the main
memory. This reduces communication through the memory controllers. Third, the
formulation breaks up the tight coupling of the explicit time stepping's
algorithmic steps to mesh traversals. This averages out data access peaks.
Different operations and algorithmic steps are ran on different grid entities.
Finally, the formulation hides distributed memory data transfer behind the
computation aligned with the mesh traversal. This reduces pressure on the
machine interconnects. All techniques applied by our formulation are elaborated
by means of a rigorous task formalism. They break up ADER-DG's tight causal
coupling of compute steps and can be generalised to other predictor-corrector
schemes.
