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

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Department of Mathematical Sciences; Center for Data Sciences


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.

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© Springer Science+Business Media, LLC 2017. Publisher's version of record: https://doi.org/10.1007/s11075-017-0364-3

Publication Title

Numerical Algorithms