Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

doi:10.1007/s10596-014-9447-6

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…The components of F with the spectral element derivatives are provided in Section 3 of Lott et al (2015). The mechanics of Newton's method is explained in detail elsewhere (Knoll and Keyes, 2004), but the key parameter that optimizes the balance between efficiency and providing consistent and robust convergence is the nonlinear convergence tolerance, Z nl .…”

Section: Solution Methodology For the Implicit Schemementioning

confidence: 99%

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Evans

Archibald

Gardner

et al. 2017

The International Journal of High Performance Computing Applica

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Explicit Runge-Kutta methods and implicit multistep methods utilizing a Newton-Krylov nonlinear solver are evaluated for a range of configurations of the shallow-water dynamical core of the spectral element community atmosphere model to evaluate their computational performance. These configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to the largest problem sizes. This analysis is performed within the shallow-water dynamical core option of a full climate model code base to enable a wealth of simulations for study, with the aim of informing solver development within the more complete hydrostatic dynamical core used for climate research. The limitations and benefits to using explicit versus implicit methods, with different parameters and settings, are discussed in light of the trade-offs with Message Passing Interface (MPI) communication and memory and their inherent efficiency bottlenecks. Given the performance behavior across the configurations analyzed here, the recommendation for future work using the implicit solvers is conditional based on scale separation and the stiffness of the problem. For the regionally refined configurations, the implicit method has about the same efficiency as the explicit method, without considering efficiency gains from a preconditioner. The potential for improvement using a preconditioner is greatest for higher spectral order configurations, where more work is shifted to the linear solver. Initial simulations with OpenACC directives to utilize a Graphics Processing Unit (GPU) when performing function evaluations show improvements locally, and that overall gains are possible with adjustments to data exchanges.

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Section: Solution Methodology For the Implicit Schemementioning

confidence: 99%

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Evans

Archibald

Gardner

et al. 2017

The International Journal of High Performance Computing Applica

View full text Add to dashboard Cite

show abstract

“…In atmospheric modeling, the propagation of fast waves -e.g., sound or gravity waves -in the system often imposes a severe stability restriction on the time step size of fully explicit schemes. Fully implicit schemes overcome this stability constraint but require solving expensive global nonlinear systems (Evans et al, 2010;Jia et al, 2013;Lott et al, 2015).…”

Section: Temporal Splittingmentioning

confidence: 99%

Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere

Hamon

Schreiber

Minion

2020

Journal of Computational Physics

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The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps, even when the terms accounting for the propagation of fast atmospheric waves are treated implicitly. Therefore, the use of parallel-in-time integration schemes to reduce the time-to-solution is of increasing interest, particularly in the numerical weather forecasting field.We present a multi-level parallel-in-time integration method combining the Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial discretization based on Spherical Harmonics (SH). The iterative algorithm computes multiple time steps concurrently by interweaving parallel highorder fine corrections and serial corrections performed on a coarsened problem. To do that, we design a methodology relying on the spectral basis of the SH to coarsen and interpolate the problem in space.The methods are evaluated on the shallow-water equations on the sphere using a set of tests commonly used in the atmospheric flow community. We assess the convergence of PFASST-SH upon refinement in time. We also investigate the impact of the coarsening strategy on the accuracy of the scheme, and specifically on its ability to capture the high-frequency modes accumulating in the solution. Finally, we study the computational cost of PFASST-SH to demonstrate that our scheme resolves the main features of the solution multiple times faster than the serial schemes.

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“…As a result, we expect IMEX MLSDC-SH to be significantly less expensive than the fully implicit SDC-SEM on a per-timestep basis for moderate resolutions. Assuming that the linear systems can be efficiently preconditioned -as in Lott et al (2015) -the key to the performance of SDC-SEM lies in its ability to take much larger stable time steps than MLSDC-SH to compensate for its relatively high cost on a per-timestep basis. Exploration of this trade-off requires a careful analysis that will be presented in future work.…”

Section: Computational Cost Of Sdc and Mlsdcmentioning

confidence: 99%

Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere

Hamon

Schreiber

Minion

2019

Journal of Computational Physics

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Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

Cited by 7 publications

References 24 publications

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere

Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere

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