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Title: Multigrid methods with space–time concurrency

Abstract

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.

Authors:
 [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:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1413170
Report Number(s):
LLNL-JRNL-678572
Journal ID: ISSN 1432-9360
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computing and Visualization in Science
Additional Journal Information:
Journal Volume: 18; Journal Issue: 4-5; Journal ID: ISSN 1432-9360
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Multigrid methods; Space–time discretizations; Parallel-in-time integration

Citation Formats

Falgout, R. D., Friedhoff, S., Kolev, Tz. V., MacLachlan, S. P., Schroder, J. B., and Vandewalle, S. Multigrid methods with space–time concurrency. United States: N. p., 2017. Web. doi:10.1007/s00791-017-0283-9.
Falgout, R. D., Friedhoff, S., Kolev, Tz. V., MacLachlan, S. P., Schroder, J. B., & Vandewalle, S. Multigrid methods with space–time concurrency. United States. doi:10.1007/s00791-017-0283-9.
Falgout, R. D., Friedhoff, S., Kolev, Tz. V., MacLachlan, S. P., Schroder, J. B., and Vandewalle, S. Fri . "Multigrid methods with space–time concurrency". United States. doi:10.1007/s00791-017-0283-9. https://www.osti.gov/servlets/purl/1413170.
@article{osti_1413170,
title = {Multigrid methods with space–time concurrency},
author = {Falgout, R. D. and Friedhoff, S. and Kolev, Tz. V. and MacLachlan, S. P. and Schroder, J. B. and Vandewalle, S.},
abstractNote = {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.},
doi = {10.1007/s00791-017-0283-9},
journal = {Computing and Visualization in Science},
number = 4-5,
volume = 18,
place = {United States},
year = {2017},
month = {10}
}

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