{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19828",
  "author_total": 4,
  "authors": [
    {
      "name": "Ivan Prusak"
    },
    {
      "name": "Enes Mustafa Soydan"
    },
    {
      "name": "Ivan Pribec"
    },
    {
      "name": "Martin Kronbichler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41wg51dbt0z7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19828",
  "fulltext_url": null,
  "id": "41wg51dbt0z7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19828",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.MS"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7213577126",
  "pdf_url": "https://arxiv.org/pdf/2609.19828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41wg51dbt0z7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements",
  "title_text": "Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/41wg51dbt0z7y",
  "venue": "arXiv",
  "versions": []
}