Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements

2026-09-17

AI Summary

本文提出了一种基于Raviart-Thomas有限元的混合精度GPU算法，用于高效模拟不可压缩湍流，通过单精度计算实现高达1.7倍加速。

Abstract

We propose GPU algorithms for high-fidelity simulation of incompressible turbulent flows. Discretization in space is performed with H(div)-conforming high-order Raviart-Thomas finite elements for the velocity and an $L^2$-conforming discontinuous Galerkin approximation for the pressure. In time, a consistent splitting scheme based on higher-order BDF time stepping is used, with convection treated explicitly. In this scheme, a pressure Poisson equation and a symmetric reaction-diffusion-type equation for the velocity need to be solved in each time step. We develop a solution framework with fast matrix-free operator evaluation for all ingredients, combined with multigrid solvers for the Poisson problem, and propose a robust mixed-precision algorithmic framework. A key to mixed-precision efficiency is a least-squares projection to generate accurate initial guesses for the iterative linear solvers, enabling us to work with relative residual tolerances of $10^{-3}$. In this regime, running the solvers entirely in single precision leads to almost no change in overall iteration counts and maintains the crucial turbulence statistics, while showing up to $1.7\times$ speedup over pure double-precision simulations.

Problem

• turbulent flow
• Raviart-Thomas finite elements
• GPU algorithms
• mixed-precision

Innovation

• mixed-precision GPU algorithms
• Raviart-Thomas finite elements
• least-squares projection
• multigrid solvers
• turbulent flow simulations