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A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLA

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  • Arteaga, Andrea
  • Ruprecht, Daniel
  • Krause, Rolf

Abstract

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.

Suggested Citation

  • Arteaga, Andrea & Ruprecht, Daniel & Krause, Rolf, 2015. "A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLA," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 727-741.
    • Handle: RePEc:eee:apmaco:v:267:y:2015:i:c:p:727-741
    DOI: 10.1016/j.amc.2014.12.055
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