A communication-avoiding implicit–explicit method for a free-surface ocean model

We examine a nonlinear elimination method for the free-surface ocean equations based on barotropic–baroclinic decomposition. The two dimensional scalar continuity equation is treated implicitly with a preconditioned Jacobian-free Newton–Krylov method (JFNK). The remaining three dimensional equations...

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Vydáno v:Journal of computational physics Ročník 305; číslo C; s. 877 - 894
Hlavní autoři: Newman, Christopher, Womeldorff, Geoffrey, Knoll, Dana A., Chacón, Luis
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Elsevier Inc 15.01.2016
Elsevier
Témata:
Algorithms
Architecture
Communication systems
Communication-avoiding algorithm
Costs
IMEX method
Jacobian-free Newton–Krylov methods
Mathematical analysis
Mathematical models
Nonlinear elimination
Nonlinearity
Ocean modeling
Three dimensional
Communication-avoiding algorithm
Ocean modeling
Jacobian-free Newton–Krylov methods
Nonlinear elimination
IMEX method
ISSN:0021-9991, 1090-2716
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Shrnutí:We examine a nonlinear elimination method for the free-surface ocean equations based on barotropic–baroclinic decomposition. The two dimensional scalar continuity equation is treated implicitly with a preconditioned Jacobian-free Newton–Krylov method (JFNK). The remaining three dimensional equations are subcycled explicitly within the JFNK residual evaluation with a method known as nonlinear elimination. In this approach, the memory footprint of the underlying Krylov vector is greatly reduced over that required by fully coupled implicit methods. The method is second-order accurate and scales algorithmically, with allowed timesteps much larger than fully explicit methods. Moreover, the hierarchical nature of the algorithm lends itself readily to emerging architectures. In particular, we introduce a communication staging strategy for the three dimensional explicit system that greatly reduces the communication costs of the algorithm and provides a key advantage as communication costs continue to dominate relative to floating point costs in emerging architectures.
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USDOE
AC52-06NA25396; LA-UR-14-26791
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.11.008