Arteaga, AndreaAndreaArteagaRuprecht, DanielDanielRuprechtKrause, RolfRolfKrause2021-10-142021-10-142015-09-15Applied Mathematics and Computation 267: 727-741 (2015-09-15)http://hdl.handle.net/11420/10523In 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.en0096-30032015727741Energy consumptionParallel-in-timePararealSpeedupSTELLAStencil computationComputer Science - Distributed; Parallel; and Cluster ComputingComputer Science - Distributed; Parallel; and Cluster ComputingMathematics - Numerical AnalysisJournal Article10.1016/j.amc.2014.12.0551409.8563v2Other