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

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 computa...

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Bibliographic Details
Published in:Numerical algorithms Vol. 78; no. 1; pp. 1 - 20
Main Authors: Ong, Benjamin W., Mandal, Bankim C.
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2018
Springer Nature B.V
Subjects:
Algebra
Algorithms
Boundary conditions
Computer Science
Decomposition
Dirichlet problem
Methods
Numeric Computing
Numerical Analysis
Original Paper
Parallel processing
Partial differential equations
Spacetime
Theory of Computation
Time dependence
Waveforms
Neumann–Neumann
Dirichlet–Neumann
Waveform relaxation
65M55
Domain decomposition
65Y05
65M20
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0364-3