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

Publikationstyp
Journal Article
Date Issued
2015-09-15
Sprache
English
Author(s)
Arteaga, Andrea  
Ruprecht, Daniel  orcid-logo
Krause, Rolf  
TORE-URI
http://hdl.handle.net/11420/10523
Journal
Applied mathematics and computation  
Volume
267
Start Page
727
End Page
741
Citation
Applied Mathematics and Computation 267: 727-741 (2015-09-15)
Publisher DOI
10.1016/j.amc.2014.12.055
Scopus ID
2-s2.0-84942991344
ArXiv ID
1409.8563v2
Peer Reviewed
true
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.
Subjects
Energy consumption
Parallel-in-time
Parareal
Speedup
STELLA
Stencil computation
Computer Science - Distributed; Parallel; and Cluster Computing
Computer Science - Distributed; Parallel; and Cluster Computing
Mathematics - Numerical Analysis