  Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles,
suffer from very stiff differential equations plus multiscale challenges in
space and time. The particles move smoothly through space until they interact
almost instantaneously due to collisions. Dense particle packings hence require
tiny time step sizes, while free particles can advance with large time steps.
Admissible time step sizes can span multiple orders of magnitudes. We propose
an adaptive local time stepping algorithm which identifies clusters of
particles that can be updated independently, advances them optimistically and
independently in time, determines collision time stamps in space-time such that
we maximise the time step sizes used, and resolves the momentum exchange
implicitly. It is combined with various acceleration techniques which exploit
multiscale geometry representations and multiscale behaviour in time. The
collision time stamp detection in space-time in combination with the implicit
solve of the actual collision equations avoids that particles get locked into
tiny time step sizes, the clustering yields a high concurrency level, and the
acceleration techniques plus local time stepping avoid unnecessary
computations. This brings a scaling, adaptive time stepping for DEM for
real-world challenges into reach.
