Computational Science – ICCS 2009

Accuracy Analysis of a Spectral Element Atmospheric Model Using a Fully Implicit Solution Framework

“…These reference solutions are solved with the FI method to a relatively tight nonlinear convergence, h n 5 10 212 . Matching simulations on the same spatial grid are performed for a range of time step sizes to isolate the temporal error, as in Evans et al (2006). These results were also calculated with a reference solution using the explicit leapfrog method run with the reference time step size, and the results were virtually unchanged.…”

“…However, assessing temporal accuracy is equally important, especially when long time integrations and transient events are considered. Significant differences in transient behavior in fluid flows can depend on the temporal convergence properties of the time integration method in the model (Evans and Knoll 2007). This section outlines each time stepping method currently implemented in HOMME to explore temporal accuracy.…”

“…It is well known that fully implicit methods need not be stability limited in the choice of time step size, and early work evaluating a preconditioned implicit time integration method for a cubed sphere shallow-water problem with a sharp front produced efficiency gains through large time step sizes on thousands of processors (Yang et al 2010). In a two-dimensional fluid flow investigation, a fully implicit integration exhibited second-order temporal accuracy and reduced time integration error for relatively large time step sizes as compared to a time-split integration (Evans et al 2006). However, this type of assessment has not yet been performed for schemes implemented in GCM components.…”

Existing Fortran interfaces to Trilinos in preparation for exascale ForTrilinos development

“…As part of the ForTrilinos project, we will enable the ACME atmosphere model (CAM) implicit solver of the fluid flow to run with demonstrated and sufficient efficiency and scalability on Summit. The solver currently utilizes a testbed ForTrilinos interface to Trilinos packages for its solution [3,7], and the work to extend it for production use within the full hydrostatic equations as part of a BER SciDAC is ongoing. Efforts to utilize the hybrid CPU-GPU Titan supercomputer at OLCF has shown significant speed-up of the residual calculation within the solver using CUDA Fortran [1], however the interface between the Fortran based residual and the C++ based Trilinos solvers prevents the data from remaining on the GPU between iterations, which more than removes the benefit of speed-up gained from the computation within the residual.…”

“…The current interface to enable Fortran/C++ interaction within CAM and a related climate application the Community Ice Sheet Model (CISM1.0) follows the developments in ForTrilinos 1.0, and the details are provided elsewhere [3,4]. CAM supports the use of the C++ based Trilinos library within this interface.…”