skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · International Journal of High Performance Computing Applications
 [1];  [1];  [2];  [1];  [3];  [2];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
+ Show Author Affiliations

In this study, 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. Finally, 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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Biological and Environmental Research (BER)
Grant/Contract Number:
AC52-07NA27344; AC05-00OR22725
OSTI ID:
1770029
Alternate ID(s):
OSTI ID: 1490619
Report Number(s):
LLNL-JRNL-716595; 859687
Journal Information:
International Journal of High Performance Computing Applications, Vol. 33, Issue 2; ISSN 1094-3420
Publisher:
SAGECopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

References (34)

AMIP Simulation with the CAM4 Spectral Element Dynamical Core journal February 2013
Spectral Transform Solutions to the Shallow Water Test Set journal June 1995
Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE journal October 2014
The Spectral Element Method for the Shallow Water Equations on the Sphere journal January 1997
Accuracy Analysis of a Spectral Element Atmospheric Model Using a Fully Implicit Solution Framework journal August 2010
The Integration of a Low Order Spectral Form of the Primitive Meteorological Equations [Low order spectral形式による primitive 方程式の積分について] journal January 1966
Short‐term time step convergence in a climate model journal February 2015
Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal January 2004
A new synoptic scale resolving global climate simulation using the Community Earth System Model journal December 2014
Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems journal January 2012
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model journal November 2011
On balanced approximations for time integration of multiple time scale systems journal March 2003
A Spectral Deferred Correction Method Applied to the Shallow Water Equations on a Sphere journal October 2013
On the Use of Finite Difference Matrix-vector Products in Newton-krylov Solvers for Implicit Climate Dynamics with Spectral Elements journal January 2015
High-Resolution Global Climate Simulations with the ECMWF Model in Project Athena: Experimental Design, Model Climate, and Seasonal Forecast Skill journal May 2012
Evaluating Performance Portability of OpenACC book January 2015
An A Posteriori–A Priori Analysis of Multiscale Operator Splitting journal January 2008
Effects of time step size on the simulation of tropical climate in NCAR-CAM3 journal January 2011
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems journal July 1986
A Scalable and Adaptable Solution Framework within Components of the Community Climate System Model book January 2009
The Parallel Performance of Standard Parabolic Marching Schemes journal March 1991
A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core journal September 2015
An initial-value problem for testing numerical models of the global shallow-water equations journal January 2004
Accelerating Time Integration for the Shallow Water Equations on the Sphere Using GPUs journal January 2015
The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity journal January 2014
An overview of the Trilinos project journal September 2005
A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates journal April 1996
The effect of time steps and time-scales on parametrization suites journal August 2012
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere journal January 2010
A compatible and conservative spectral element method on unstructured grids journal August 2010
A multidecadal simulation of Atlantic tropical cyclones using a variable-resolution global atmospheric general circulation model journal August 2014
A case study of CUDA FORTRAN and OpenACC for an atmospheric climate kernel journal July 2015
Tropical Cyclones in the UPSCALE Ensemble of High-Resolution Global Climate Models journal January 2015
A standard test set for numerical approximations to the shallow water equations in spherical geometry journal September 1992

Similar Records

Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models
Journal Article · Tue Apr 17 00:00:00 EDT 2018 · Geoscientific Model Development (Online) · OSTI ID:1770029
+3 more
Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows
Conference · Tue Jul 01 00:00:00 EDT 2008 · OSTI ID:1770029
+1 more
Acceleration of the IMplicit–EXplicit nonhydrostatic unified model of the atmosphere on manycore processors
Journal Article · Tue Oct 31 00:00:00 EDT 2017 · International Journal of High Performance Computing Applications · OSTI ID:1770029
+3 more

Related Subjects

58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
Global climate modeling
implicit methods
Newton-Krylov
regional refinement
GPU acceleration
Newton–Krylov