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Title: Multigrid methods with space–time concurrency

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporal dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.
 [1] ;  [2] ;  [1] ;  [3] ;  [1] ;  [4]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. KU Leuven Leuven (Belgium); Bergische Univ. Wuppertal, Wuppertal (Germany)
  3. Memorial Univ. of Newfoundland, St. John's (Canada)
  4. KU Leuven Leuven (Belgium)
Publication Date:
Report Number(s):
Journal ID: ISSN 1432-9360
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Computing and Visualization in Science
Additional Journal Information:
Journal Volume: 18; Journal Issue: 4-5; Journal ID: ISSN 1432-9360
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Multigrid methods; Space–time discretizations; Parallel-in-time integration
OSTI Identifier: