project-c1

A Multi-Scale and Multi-Physics Time Integration Approach

Publications

• Many-Stage Optimal Stabilized Runge–Kutta Methods for Hyperbolic Partial Differential Equations.
  Doehring, Gassner, Torrilhon. Journal of Scientific Computing. 2024/04.
  DOI: 10.1007/s10915-024-02478-5
  Software:

  1. OSPREI: Code for generating Optimal Stability Polynomials in Roots for Explicit time Integration.
     Github

• Multirate Time-Integration based on Dynamic ODE Partitioning through Adaptively Refined Meshes for Compressible Fluid Dynamics.
  Doehring, Schlottke-Lakemper, Gassner, Torrilhon. Journal of Computational Physics. 2024/10.
  DOI: 10.1016/j.jcp.2024.113223
  Software:

  1. Reproducibility Repository.
     Github
  2. SSOCs: Arbitrary Precision Stability Polynomials by Second-Order Cones.
     Github

• Fourth-Order Paired-Explicit Runge-Kutta Methods. Doehring, Christmann, Schlottke-Lakemper, Gassner, Torrilhon. Computational Science and Engineering. 2025/10.
  DOI: 10.1007/s44207-025-00005-4
  Software:

  1. Reproducibility Repository.
     Github

• Paired Explicit Relaxation Runge-Kutta Methods: Entropy Conservative/Stable High-Order Optimized Multirate Time Integration.
  Doehring, Ranocha, Torrilhon. Arxiv Preprint. 2025/07.
  DOI: 10.48550/arXiv.2507.04991
  Software:

  1. Reproducibility Repository.
     Github

Contributions to Major Open Source Projects

• Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia
  Github Contributions
• Ipopt: COIN-OR Interior Point Optimizer IPOPT
  Github Contributions

Misc

• Slides: Github
• Video of Talk at JuliaCon 2024: https://www.youtube.com/watch?v=dPk51HGzsZk&t=1350s