A Holistic Algorithmic Approach to Improving Accuracy, Robustness, and Computational Efficiency for Atmospheric Dynamics

Abstract

Atmospheric weather and climate models must perform simulations very quickly to be useful. Therefore, modelers have traditionally focused on reducing computations as much as possible. However, in our new era of increasingly compute-capable hardware, data movement is now the prohibiting expense. This study examines the computational benefits of a new algorithmic approach to modeling atmospheric dynamics on scales relevant to weather and climate simulation. Rather than minimizing computations, this new approach considers the larger problem more holistically, including spatial accuracy, temporal accuracy, robustness (i.e., oscillations), on-node efficiency, and internode data transfers together at once. Numerical experiments demonstrate how computations can be strategically increased to simultaneously address each of these constraints while reducing data movement to adapt to modern accelerated hardware. The new algorithm can achieve at times up to 80\% peak floating point throughput in single precision on the Nvidia Tesla V100 GPU, where the traditional approach is shown to only achieve single-digit floating point efficiency. Further, the new algorithm is twice as fast as a standard Runge-Kutta time integrator, and high-order accuracy with Weighted Essentially Non-Oscillatory (WENO) limiting came at less than 30\% additional runtime cost on a GPU, thus increasing the accuracy per degree of freedom.

A high‐order WENO‐limited finite‐volume algorithm for atmospheric flow using the ADER‐differential transform time discretization

“…Note the domains of P L , P C , and P R all overlap in the center cell. Note this figure also appears in Norman and Larkin (2020)…”

“…High‐order‐accurate methods and WENO limiting improve on this because they increase computations without significantly increasing data movement. This is true even for small GPU workloads (see section 5.1.4 of Norman and Larkin (2020)).…”

“…Kinetic energy is calculated as . Note that a similar study is performed in Norman and Larkin (2020), but that plot was too noisy to draw robust conclusions. Here, the results are averaged over many time steps and vertical levels to produce something smooth enough for clear comparison.…”

“…While a detailed description of the code's C++ performance portable implementation and analysis of this code's performance on GPU accelerators is given in Norman and Larkin (2020), it is worth mentioning a few interesting computational findings. GPUs typically have memory bandwidth rates (the amount of data that can be transferred per second) that are much higher than those of CPUs.…”

“…Note the domains of P L , P C , and P R all overlap in the center cell. Note this figure also appears in Norman and Larkin (2020) [Colour figure can be viewed at wileyonlinelibrary.com] of Norman and Nair (2018), which is similar in nature to the WENO implementations in (Capdeville, 2008a;2008b;Norman, 2015b). In this approach, all of the polynomial coefficients are explicitly formed, and the WENO-limited polynomial is a weighted combination of the lower-order polynomials.…”