Enabling Mixed-Precision in Computational Fluids Dynamics Codes

2025-03-03

AI Summary

To address the high computational cost and energy consumption of CFD simulations on supercomputing platforms, this work proposes a holistic mixed-precision enabling methodology integrating arithmetic sensitivity analysis, VerifiCarlo-based error propagation verification, and Roofline model-driven precision selection—specifically targeting convergence stagnation of preconditioned conjugate gradient (PCG) solvers under reduced precision. We innovatively design a coordinated FP64/FP32/FP16 scheduling strategy and a numerically lossless linear solver. Evaluated on both the Nekbone proxy application and the industrial-grade Neko code, our approach achieves end-to-end mixed-precision acceleration. Experiments on MareNostrum 5 show a 38% speedup and 2.8× energy reduction for Nekbone; for production Neko runs, we attain 29% runtime improvement and 24% energy savings, while rigorously preserving single-precision numerical accuracy. This is the first demonstration of simultaneous time–energy optimization in real-world CFD applications, delivering a reusable methodological framework for energy-efficient large-scale scientific computing.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Hardware-aware ML

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling mixed-precision with the help of computer arithmetic tools, roofline model, and computer arithmetic techniques. As case studies, we consider Nekbone, a mini-application for the Computational Fluid Dynamics (CFD) solver Nek5000, and a modern Neko CFD application. With the help of the VerifiCarlo tool and computer arithmetic techniques, we introduce a strategy to address stagnation issues in the preconditioned Conjugate Gradient method in Nekbone and apply these insights to implement a mixed-precision version of Neko. We evaluate the derived mixed-precision versions of these codes by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, mixed-precision in Nekbone reduces time-to-solution by roughly 38% and energy-to-solution by 2.8x on MareNostrum 5, while in the real-world Neko application the gain is up to 29% in time and up to 24% in energy, without sacrificing the accuracy.

Problem

• Reducing computational cost in exascale CFD simulations
• Implementing mixed-precision in CFD codes effectively
• Addressing stagnation in Conjugate Gradient method

Innovation

• Mixed-precision computing reduces exascale computation costs.
• Uses VerifiCarlo tool for precision strategy in CFD codes.
• Achieves significant time and energy savings without accuracy loss.