Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements
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 L2-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× speedup over pure double-precision simulations.
Related
- Comb Tensor Network Finite-Difference Time-Domain Algorithms for 2D and 3D Electromagnetic Simulations
- Efficient Algorithms for Energy-Aware Single-Machine Scheduling with Battery Storage
- A Novel Matrix-Free Approximate Elemental Inverse for Efficient Preconditioning of Discontinuous Galerkin Spectral Elements
- Sparse Dictionary Learning for Measure-Valued Data via Linearized Optimal Transport: Efficient Algorithms and Sample Complexity
- Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters
BibTeX
@misc{prusak2026mixedprecision,
title = {{Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements}},
author = {Ivan Prusak and Enes Mustafa Soydan and Ivan Pribec and Martin Kronbichler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19828},
eprint = {2609.19828},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19828},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements
AU - Ivan Prusak
AU - Enes Mustafa Soydan
AU - Ivan Pribec
AU - Martin Kronbichler
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19828
UR - https://arxiv.org/abs/2609.19828
AB - 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× speedup over pure double-precision simulations.
ER -