Pipeline implementations of Neumann–Neumann and Dirichlet–Neumann waveform relaxation methods

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Abstract

This paper is concerned with the reformulation of Neumann–Neumann waveform relaxation (NNWR) methods and Dirichlet–Neumann waveform relaxation (DNWR) methods, a family of parallel space-time approaches to solving time-dependent PDEs. By changing the order of the operations, pipeline-parallel computation of the waveform iterates are possible, without changing the solution of each waveform iterate. The parallel efficiency of the pipeline implementation is analyzed, as well as the change in the communication pattern. Numerical studies are presented to show the effectiveness of the pipeline NNWR and DNWR algorithms.

Keywords

Dirichlet–Neumann Neumann–Neumann Waveform relaxation Domain decomposition 

Mathematics Subject Classification (2010)

65M55 65Y05 65M20 

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Notes

Acknowledgments

This work utilized computational resources provided by superior, the high-performance computing cluster MTU, and by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Mathematical SciencesMichigan Technological UniversityHoughtonUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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