Scalable algorithms for massively parallel computers

Tracer transport simulation
Illustration of the accuracy of simulating three-dimensional atmospheric transport over mountainlike terrain in an idealized global atmosphere. In this case the terrain is a concentric series of idealized mountain ranges expanding out from the equator and 80 degrees east longitude. This figure shows the vertical cross-section along the equator of a tracer field at three different simulation times (with day 0 being the starting condition). The black-filled sections indicate the physical topography at the surface, and the black lines indicate how the horizontal lines of the numerical grid adapt to this topography. The idealized atmospheric flow is just a constant, solid-body rotation, and the tracer field is represented by the three thin vertically stacked cloud-like patches. These concentrations should circumnavigate the globe and return to their initial positions after 12 days, so a perfect simulation would result in the tracer field returning exactly to its original position and concentrations in that time. Some spreading of the tracer concentrations over space appears, but the modest size of these numerical artifacts and the difficulty of this test case show a state-of-the-art transport computation. The results are computed with the non-hydrostatic formulation of HOMME that is being developed for the next-generation dynamical core of the NCAR atmosphere model.

NCAR models of the Earth System, the Sun, and the Sun-Earth System motivate CISL’s scientific research on algorithms, numerical methods, and computational performance.

A priority in geophysical modeling is to increase resolution because higher resolution can resolve important processes to improve the accuracy of prediction and perhaps uncover unexpected interactions within the physical system.

This goal must be pursued within the context of massively parallel hardware that are the now the norm for high performance computing environments.

Given these two elements, CISL research focuses on areas to increase model resolution through methods that scale to large numbers of processors or coprocessors.

Improvements in simulation speed on these large systems depend on better numerical algorithms and innovative application of computer science.

Moreover, many of these new strategies arise as basic scientific research on idealized problems and are later transferred to the practical requirements of NCAR community models.

Some highlights from 2015 include:

  • Steady progress was made on creating a nonhydrostatic and three- dimensional dynamical core (HOMAM) for the NCAR Community Atmosphere Model. Among its significant accomplishments, this new model was able to reproduce gravity wave tests with accuracy that matches standard benchmarks for comparing dynamical cores.

  • Radial basis functions were successfully applied to represent the Earth’s surface topography as a boundary condition for the electric field in the Earth’s atmosphere. This work highlights the application of “meshless” methods for problems that involve irregular boundaries such as coastlines and irregular surface features.

This work is funded as specified in the following individual reports.

Under a separate grant from the NSF, Dr. Natasha Flyer (IMAGe) in collaboration with Dr. Bengt Fornberg (University of Colorado) published the SIAM (Society of Industrial and Applied Mathematics) monograph A Primer on Radial Basis Functions with Applications to the Geosciences. This book serves an introduction to numerical methods that are not constrained to regular grids, and it pioneers their application to numerical models commonly encountered in the Earth System. Besides the numerical accuracy of radial basis techniques, they are also easy to program. Algorithms that use these methods do not require complex coding and so are well suited to parallelization on GPUs and other coprocessors.