Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 41 min ago
PreprintCC BY 4.0arXiv

Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation

  • Santolo Leveque
  • Luca Bergamaschi
  • Ángeles Martínez
  • Erin Carson
Open at sourcePDFDOICite

Abstract

We study the effect of mixed precision on the numerical integration of the heat equation discretized with a Runge--Kutta method in time. A full space-time discretization is applied, which results in a very large and sparse linear system to be solved for the numerical approximations and the Runge--Kutta stages of all time steps. The linear system is solved by applying a suitable preconditioned iterative method that can be run in parallel. In order to speed up the solution process, the preconditioner is applied using a mixed precision framework. Sequential results show the robustness of the preconditioner, even when applied in mixed precision. Finally, we present numerical evidence of the improved performance of the mixed precision strategy when applied in a parallel environment, achieving up to a 50% reduction in CPU time.

Related

  1. Scalable Fully Implicit Runge-Kutta Solvers for Time-Dependent Rayleigh-Bénard Convection
    Ahsan Ali, Robert C. Kirby
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers
    Xing Guo, Hongwei Tang, Zewei Meng +3
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingFluid dynamicsarXiv
  3. A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations
    Yi Zhang
    arXivPreprintarXiv licenceFull textMathematical physicsNumerical analysis & scientific computingarXiv
  4. Integrable full discretization of the multi-component short pulse equation
    Ayako Hori, Yuta Tanaka, Ken-ichi Maruno +2
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv
  5. Mixed finite element discretization of intrinsic geometrically exact beams for multiplier-free multibody dynamics
    Andrea Brugnoli, Philipp L. Kinon, Francesco Sanfedino +2
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingComputational physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{leveque2026mixed,
  title = {{Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation}},
  author = {Santolo Leveque and Luca Bergamaschi and Ángeles Martínez and Erin Carson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16863},
  eprint = {2609.16863},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16863},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation
AU  - Santolo Leveque
AU  - Luca Bergamaschi
AU  - Ángeles Martínez
AU  - Erin Carson
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16863
UR  - https://arxiv.org/abs/2609.16863
AB  - We study the effect of mixed precision on the numerical integration of the heat equation discretized with a Runge--Kutta method in time. A full space-time discretization is applied, which results in a very large and sparse linear system to be solved for the numerical approximations and the Runge--Kutta stages of all time steps. The linear system is solved by applying a suitable preconditioned iterative method that can be run in parallel. In order to speed up the solution process, the preconditioner is applied using a mixed precision framework. Sequential results show the robustness of the preconditioner, even when applied in mixed precision. Finally, we present numerical evidence of the improved performance of the mixed precision strategy when applied in a parallel environment, achieving up to a 50% reduction in CPU time.
ER  -