Summation-by-parts operators for correction procedure via reconstruction. - Hendrik Ranocha; Philipp Öffner; Thomas Sonar (J. Comput. Phys., 2016)

Extended skew-symmetric form for summation-by-parts operators and varying Jacobians. - Hendrik Ranocha; Philipp Öffner; Thomas Sonar (J. Comput. Phys., 2017)

Advantages and pitfalls of OpenCL in computational physics. - Katharina Ostaszewski; Philip Heinisch; Hendrik Ranocha (IWOCL, 2018)

Generalised summation-by-parts operators and variable coefficients. - Hendrik Ranocha (J. Comput. Phys., 2018)

Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations. - Hendrik Ranocha (J. Sci. Comput., 2018)

L2 Stability of Explicit Runge-Kutta Schemes. - Hendrik Ranocha; Philipp Öffner (J. Sci. Comput., 2018)

Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes. - Rémi Abgrall; Philipp Öffner; Hendrik Ranocha (CoRR, 2019)

Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators. - Hendrik Ranocha; Katharina Ostaszewski; Philip Heinisch (CoRR, 2019)

Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems. - Hendrik Ranocha; David I. Ketcheson (CoRR, 2019)

On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navie-Stokes equations. - Diego Rojas; Radouan Boukharfane; Lisandro Dalcín; David C. Del Rey Fernández; Hendrik Ranocha; David E. Keyes; Matteo Parsani (CoRR, 2019)

Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients. - Philipp Öffner; Hendrik Ranocha (J. Sci. Comput., 2019)

Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations. - Hendrik Ranocha; Lisandro Dalcín; Matteo Parsani (Comput. Math. Appl., 2020)

Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL. - Philip Heinisch; Katharina Ostaszewski; Hendrik Ranocha (CoRR, 2020)

A Class of A Stable Summation by Parts Time Integration Schemes. - Hendrik Ranocha; Jan Nordström (CoRR, 2020)

Positivity-Preserving Adaptive Runge-Kutta Methods. - Stephan Nüßlein; Hendrik Ranocha; David I. Ketcheson (CoRR, 2020)

A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations. - Hendrik Ranocha; Dimitrios Mitsotakis; David I. Ketcheson (CoRR, 2020)

A conservative fully-discrete numerical method for the regularised shallow water wave equations. - Dimitrios Mitsotakis; Hendrik Ranocha; David I. Ketcheson; Endre Süli (CoRR, 2020)

Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes. - Hendrik Ranocha; Gregor J. Gassner (CoRR, 2020)

RK-Opt: A package for the design of numerical ODE solvers. - David I. Ketcheson; Matteo Parsani; Zachary Grant; Aron J. Ahmadia; Hendrik Ranocha (J. Open Source Softw., 2020)

NodePy: A package for the analysis of numerical ODE solvers. - David I. Ketcheson; Hendrik Ranocha; Matteo Parsani; Umair bin Waheed; Yiannis Hadjimichael (J. Open Source Softw., 2020)

Relaxation Runge-Kutta Methods for Hamiltonian Problems. - Hendrik Ranocha; David I. Ketcheson (J. Sci. Comput., 2020)

General relaxation methods for initial-value problems with application to multistep schemes. - Hendrik Ranocha; Lajos Lóczi; David I. Ketcheson (Numerische Mathematik, 2020)

Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems. - Hendrik Ranocha; David I. Ketcheson (SIAM J. Numer. Anal., 2020)

Relaxation Runge-Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations. - Hendrik Ranocha; Mohammed Sayyari; Lisandro Dalcín; Matteo Parsani; David I. Ketcheson (SIAM J. Sci. Comput., 2020)

On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations. - Hendrik Ranocha; Manuel Quezada de Luna; David I. Ketcheson (CoRR, 2021)

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics. - Hendrik Ranocha; Lisandro Dalcín; Matteo Parsani; David I. Ketcheson (CoRR, 2021)

Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. - Hendrik Ranocha; Michael Schlottke-Lakemper; Andrew R. Winters; Erik Faulhaber; Jesse Chan; Gregor J. Gassner (CoRR, 2021)

A New Stability Approach for Positivity-Preserving Patankar-type Schemes. - Davide Torlo; Philipp Öffner; Hendrik Ranocha (CoRR, 2021)

On the robustness and performance of entropy stable collocated discontinuous Galerkin methods. - Diego Rojas; Radouan Boukharfane; Lisandro Dalcín; David C. Del Rey Fernández; Hendrik Ranocha; David E. Keyes; Matteo Parsani (J. Comput. Phys., 2021)

A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. - Michael Schlottke-Lakemper; Andrew R. Winters; Hendrik Ranocha; Gregor J. Gassner (J. Comput. Phys., 2021)

SummationByPartsOperators.jl: A Julia library of provably stable discretization techniques with mimetic properties. - Hendrik Ranocha (J. Open Source Softw., 2021)

Kinetic Functions for Nonclassical Shocks, Entropy Stability, and Discrete Summation by Parts. - Philippe G. LeFloch; Hendrik Ranocha (J. Sci. Comput., 2021)

A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions. - Hendrik Ranocha; Jan Nordström (J. Sci. Comput., 2021)

A Conservative Fully Discrete Numerical Method for the Regularized Shallow Water Wave Equations. - Dimitrios Mitsotakis; Hendrik Ranocha; David I. Ketcheson; Endre Süli (SIAM J. Sci. Comput., 2021)

A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations. - Hendrik Ranocha (CoRR, 2022)

On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows. - Jesse Chan; Hendrik Ranocha; Andrés M. Rueda-Ramírez; Gregor Gassner; Tim Warburton (CoRR, 2022)

On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics. - Hendrik Ranocha; Andrew R. Winters; Hugo Guillermo Castro; Lisandro Dalcín; Michael Schlottke-Lakemper; Gregor J. Gassner; Matteo Parsani (CoRR, 2022)

Bridging HPC Communities through the Julia Programming Language. - Valentin Churavy; William F. Godoy; Carsten Bauer; Hendrik Ranocha; Michael Schlottke-Lakemper; Ludovic Räss; Johannes P. Blaschke; Mosè Giordano; Erik Schnetter; Samuel Omlin; Jeffrey S. Vetter; Alan Edelman (CoRR, 2022)

Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: Application to structure preserving discretization. - Rémi Abgrall; Philipp Öffner; Hendrik Ranocha (J. Comput. Phys., 2022)

A note on numerical fluxes conserving a member of Harten's one-parameter family of entropies for the compressible Euler equations. - Hendrik Ranocha (J. Comput. Phys., 2022)

Reproducibility repository for Bridging HPC Communities through the Julia Programming Language. - Valentin Churavy; William F. Godoy; Carsten Bauer; Hendrik Ranocha; Michael Schlottke-Lakemper; Ludovic Räss; Johannes P. Blaschke; Mosè Giordano; Erik Schnetter; Samuel Omlin; Jeffrey S. Vetter; Alan Edelman (Zenodo, 2022)

Resolving Entropy Growth from Iterative Methods. - Viktor Linders; Hendrik Ranocha; Philipp Birken (CoRR, 2023)

Stability of step size control based on a posteriori error estimates. - Hendrik Ranocha; Jan Giesselmann (CoRR, 2023)

Functional-preserving predictor-corrector multiderivative schemes. - Hendrik Ranocha; Jochen Schütz; Eleni Theodosiou (CoRR, 2023)

Multiderivative time integration methods preserving nonlinear functionals via relaxation. - Hendrik Ranocha; Jochen Schütz (CoRR, 2023)

High-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (CoRR, 2023)

Step size control for explicit relaxation Runge-Kutta methods preserving invariants. - Sebastian Bleecke; Hendrik Ranocha (CoRR, 2023)

Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar-Runge-Kutta Methods. - Thomas Izgin; Hendrik Ranocha (CoRR, 2023)

Computing with B-series. - David I. Ketcheson; Hendrik Ranocha (ACM Trans. Math. Softw., 2023)

A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators. - Hendrik Ranocha (J. Comput. Phys., 2023)

Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws. - Hendrik Ranocha; Michael Schlottke-Lakemper; Jesse Chan; Andrés M. Rueda-Ramírez; Andrew R. Winters; Florian Hindenlang; Gregor J. Gassner (ACM Trans. Math. Softw., 2023)

Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations. - Joshua Lampert; Hendrik Ranocha (CoRR, 2024)

Structure-Preserving Numerical Methods for Fokker-Planck Equations. - Hanna Bartel; Joshua Lampert; Hendrik Ranocha (CoRR, 2024)

Pseudo-Energy-Preserving Explicit Runge-Kutta Methods. - Gabriel A. Barrios de León; David I. Ketcheson; Hendrik Ranocha (CoRR, 2024)

Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form. - Hendrik Ranocha; Mario Ricchiuto (CoRR, 2024)

GeophysicalModelGenerator.jl: A Julia package to visualise geoscientific data and create numerical model setups. - Boris J. P. Kaus; Marcel Thielmann; Pascal Aellig; Albert de Montserrat; Luca de Siena; Jacob Frasukiewicz; Lukas Fuchs; Andrea Piccolo; Hendrik Ranocha; Nicolas Riel; Christian Schuler; Arne Spang; et al. (J. Open Source Softw., 2024)

HOHQMesh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements. - David A. Kopriva; Andrew R. Winters; Michael Schlottke-Lakemper; Joseph A. Schoonover; Hendrik Ranocha (J. Open Source Softw., 2024)

Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. - Jan Glaubitz; Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Gregor Gassner (J. Comput. Phys., 2025)

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (J. Comput. Phys., 2025)

Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs. - Cordula Reisch; Hendrik Ranocha (SIAM Rev., 2025)

t8code - modular adaptive mesh refinement in the exascale era. - Johannes Holke; Johannes Markert; David Knapp; Lukas Dreyer; Sandro Elsweijer; Niklas Böing; Ioannis Lilikakis; Jakob Fussbroich; Tabea Leistikow; Florian Becker; Veli Uenlue; Ole Albers; et al. (J. Open Source Softw., 2025)

Automatic differentiation for Lax-Wendroff-type discretizations. - Arpit Babbar; Valentin Churavy; Michael Schlottke-Lakemper; Hendrik Ranocha (CoRR, 2025)

PositiveIntegrators.jl: A Julia library of positivity-preserving time integration methods. - Stefan Kopecz; Joshua Lampert; Hendrik Ranocha (J. Open Source Softw., 2025)

Traveling-Wave Solutions and Structure-Preserving Numerical Methods for a Hyperbolic Approximation of the Korteweg-de Vries Equation. - Abhijit Biswas; David I. Ketcheson; Hendrik Ranocha; Jochen Schütz (J. Sci. Comput., 2025)

Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration. - Daniel Doehring; Hendrik Ranocha; Manuel Torrilhon (CoRR, 2025)

Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators. - Wasilij Barsukow; Christian Klingenberg; Lisa Lechner; Jan Nordström; Sigrun Ortleb; Hendrik Ranocha (CoRR, 2025)

Real-time rail vehicle localisation using spatially resolved magnetic field measurements. - Niklas Dieckow; Katharina Ostaszewski; Philip Heinisch; Henriette Struckmann; Hendrik Ranocha (CoRR, 2025)

Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions. - Jan Giesselmann; Hendrik Ranocha (CoRR, 2025)

The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable. - Louis Petri; Gunnar Birke; Christian Engwer; Hendrik Ranocha (CoRR, 2025)