  In view of the rapid rise of the number of cores in modern supercomputers,
time-parallel methods that introduce concurrency along the temporal axis are
becoming increasingly popular. For the solution of time-dependent partial
differential equations, these methods can add another direction for concurrency
on top of spatial parallelization. The paper presents an implementation of the
time-parallel Parareal method in a C++ domain specific language for stencil
computations (STELLA). STELLA provides both an OpenMP and a CUDA backend for a
shared memory parallelization, using the CPU or GPU inside a node for the
spatial stencils. Here, we intertwine this node-wise spatial parallelism with
the time-parallel Parareal. This is done by adding an MPI-based implementation
of Parareal, which allows us to parallelize in time across nodes. The
performance of Parareal with both backends is analyzed in terms of speedup,
parallel efficiency and energy-to-solution for an advection-diffusion problem
with a time-dependent diffusion coefficient.
