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Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
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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 15 Pith papers
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Admissible Lax-Wendroff Flux Reconstruction Method with Automatic Differentiation on Adaptive Curved Meshes for Relativistic Hydrodynamics
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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
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Gaussian FSBP operators: Comparison and application to numerical methods for hyperbolic conservation laws
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Characterizing electronic scattering rates with transport in multiterminal devices
A linearized Boltzmann model in five-terminal geometry shows current partition diagnoses ballistic-hydrodynamic-Ohmic crossover and extracts momentum-relaxing and conserving scattering rates.
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Characterizing electronic scattering rates with transport in multiterminal devices
A five-terminal geometry diagnoses ballistic-hydrodynamic-Ohmic crossovers and extracts momentum-relaxing and conserving scattering rates from current partition in electron liquids.
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Characterizing electronic scattering rates with transport in multiterminal devices
Current partition in a five-terminal geometry diagnoses ballistic-hydrodynamic-Ohmic crossovers and extracts momentum-relaxing and conserving scattering rates in 2D electron systems.
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Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration
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.
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Adaptive Multiphysics Coupling for Hyperbolic Systems
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.
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Convergence analysis of structure-preserving schemes for the multicomponent compressible Euler flows
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ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
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Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
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