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Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing

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arxiv 2108.06476 v2 pith:WIMEQQ4F submitted 2021-08-14 cs.MS cs.NAmath.NAphysics.comp-ph

Hendrik Ranocha , Michael Schlottke-Lakemper , Andrew R. Winters , Erik Faulhaber , Jesse Chan , Gregor J. Gassner This is my paper
classification cs.MScs.NAmath.NAphysics.comp-ph
keywords juliatrixicomputingnumericaladaptivefortranscientificsimulations
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We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible, easy to use, and fast. We describe the main design choices that enable these features and compare Trixi.jl with a mature open source Fortran code that uses the same numerical methods. We conclude with an assessment of Julia for simulation-focused scientific computing, an area that is still dominated by traditional high-performance computing languages such as C, C++, and Fortran.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods

    math.NA 2025-08 accept novelty 7.0 of 10

    The authors derive an entropy-conservative two-point flux for the ultra-relativistic Euler equations, prove its consistency, and validate an entropy-stable DG scheme against 1D radial reference solutions in 2D and 3D.

  2. Gaussian FSBP operators: Comparison and application to numerical methods for hyperbolic conservation laws

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    Open generalized Gaussian quadrature points produce summation-by-parts operators with fewer points than closed rules for the same non-polynomial function space, at the cost of boundary extrapolation; the resulting sch...

  3. Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration

    math.NA 2025-07 accept novelty 6.0 of 10

    Paired Explicit Relaxation Runge-Kutta (P-ERRK) methods give entropy-stable multirate time integration for compressible flows, with measured speedups of 3-4x over standalone relaxed schemes.

  4. Adaptive Multiphysics Coupling for Hyperbolic Systems

    math.NA 2026-07 conditional novelty 5.0 of 10

    Trixi.jl gains adaptive multiphysics coupling via boundary exchange and user coupling functions, with runtime model switching that cuts cost versus full complex-model runs.

  5. ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

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    ATHENA introduces an agentic team framework that autonomously manages the end-to-end computational research lifecycle via a knowledge-driven HENA loop to achieve validation errors of 10^{-14} in scientific computing a...

  6. Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting

    math.NA 2025-07 conditional novelty 5.0 of 10

    A quadratic knapsack objective for subcell limiting in entropy-stable DG methods is reduced to finite-iteration scalar root-finding and shown to improve temporal regularity and reduce adaptive timestep counts.

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