CEED project examines scalability and performance of key algorithms for HPC applications

Researchers working with the Exascale Computing Project’s Center for Efficient Exascale Discretization recently published findings of investigations they conducted into performance trade-offs for compute-intensive kernels in scientific computing applications. Large-scale numerical solvers must be optimized to ensure efficient high-performance, particularly when scaling to high processor counts. Their work established community benchmarks for a set of operations (i.e., operator evaluation in iterative solution of linear systems) that are common to many simulation codes used in nuclear reactor modeling, additive manufacturing, compressible flow, wind energy, and climate modeling. Results were published in the June 15, 2020, online edition of the International Journal of High Performance Computing Applications.

Many science and engineering simulations require the solution of very large systems of equations to approximate physical quantities of interest at computational gridpoints in the domain of interest, such as the velocity, temperature, and pressure inside a reactor. With more gridpoints, larger domains and/or fixed domains can be explored in greater detail. The computational cost is proportional to the number of gridpoints, which can be in the trillions at exascale.

The published work brought together several teams from around the world, each with decades of experience on the world’s fastest supercomputers, in a bake-off competition aimed at developing  high-order methods to reduce the problem size for a given accuracy and ensuring that the cost per gridpoint for the high-order method is the same or less than that of traditional low-order methods. To arrive at recommendations for best practices for assessing runtime efficiency, the researchers measured peak performance (i.e., degrees of freedom per second) and identified effective code optimization strategies for multiple codes and platforms.

Through this effort and continued direct comparisons on more recent architectures, the researchers have significantly reduced computing costs for those working in reactor design, combustion, aerosol transport, turbulence research, and other energy-related fields. The research has also helped computer vendors identify hot spots that can be remedied to improve overall simulation performance. Although the work focused on a particular set of operations, the team’s performance analysis is equally applicable to a broad spectrum of numerical partial differential equation discretizations, including finite difference, finite volume, and h‑type finite elements. Their benchmark data will be used to guide future software and hardware development.


Fischer, Paul, Misun Min, Thilina Rathnayake, Som Dutta, Tzanio Kolev, Veselin Dobrev, Jean-Sylvain Camier, et al. 2020. “Scalability of High-Performance PDE Solvers.” The International Journal of High Performance Computing Applications 34 (5) (June 15): 562–586. doi:10.1177/1094342020915762. http://dx.doi.org/10.1177/1094342020915762.