• 2022
• 2021
• 2020
• 2019
• 2018
• 2017
• 2016
• 2015

2022

• Ranocha, H. 2022. A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations,
• Abgrall, R, Öffner, P, and Ranocha, H. 2022. “Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization.” Journal of Computational Physics, № 2022: 110955. doi: 10.1016/j.jcp.2022.110955.
• Ranocha, H, Schlottke-Lakemper, M, Winters, AR, Faulhaber, E, Chan, J, and Gassner, G. 2022. “Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing.” Proceedings of the JuliaCon Conferences, № 1 (1): 77. doi: 10.21105/jcon.00077.

2021

• Schlottke-Lakemper, M, Winters, AR, Ranocha, H, and Gassner, GJ. 2021. “A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.” Journal of Computational Physics, № 2021: 110467. doi: 10.1016/j.jcp.2021.110467.
• Mitsotakis Dimitrios, Ranocha Hendrik, and Ketcheson David I, Süli Endre. 2021. “A conservative fully-discrete numerical method for the regularized shallow water wave equations.” SIAM Journal on Scientific Computing, № 42 doi: 10.1137/20M1364606.
• LeFloch, PG, and Ranocha, H. 2021. “Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts.” Journal of Scientific Computing, № 87 doi: 10.1007/s10915-021-01463-6.
• Ranocha, H, and Nordström, J. 2021. “A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions.” Journal of Scientific Computing, № 87 doi: 10.1007/s10915-021-01454-7.
• Ranocha, H, Mitsotakis, D, and Ketcheson, DI. 2021. “A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations.” Communications in Computational Physics, № 29 (4): 979–1029. doi: 10.4208/cicp.OA-2020-0119.
• Ranocha, H. 2021. “On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators.” IMA Journal of Numerical Analysis, № 41 (1): 654–682. doi: 10.1093/imanum/drz070.
• Rojas, D, Boukharfane, R, Dalcin, L, Fernández, DCDR, Ranocha, H, Keyes, DE, and Parsani, M. 2021. “On the robustness and performance of entropy stable discontinuous collocation methods.” Journal of Computational Physics, № 426: 109891. doi: 10.1016/j.jcp.2020.109891.
• Ranocha, H, Schlottke-Lakemper, M, Chan, J, Rueda-Ramírez, AM, Winters, AR, Hindenlang, F, and Gassner, GJ. 2021. Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws,
• Ketcheson, DI, and Ranocha, H. 2021. Computing with B-series,
• Torlo, D, Öffner, P, and Ranocha, H. 2021. A New Stability Approach for Positivity-Preserving Patankar-type Schemes,
• Ranocha, H, Dalcin, L, Parsani, M, and Ketcheson, DI. 2021. “Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.” Communications on Applied Mathematics and Computation, № 2021 doi: 10.1007/s42967-021-00159-w.
• Nüßlein, S, Ranocha, H, and Ketcheson, DI. 2021. “Positivity-Preserving Adaptive Runge-Kutta Methods.” Communications in Applied Mathematics and Computational Science, № 16 (2): 155–179. doi: 10.2140/camcos.2021.16.155.
• Ranocha, H, Luna, M, and Ketcheson, DI. 2021. “On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations.” Partial Differential Equations and Applications, № 2 (6): 76. doi: 10.1007/s42985-021-00126-3.
• Ranocha, H. 2021. “SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties.” Journal of Open Source Software, № 6 (64): 3454. doi: 10.21105/joss.03454.
• Ranocha, H, and Gassner, GJ. 2021. “Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes.” Communications on Applied Mathematics and Computation, № 2021 doi: 10.1007/s42967-021-00148-z.
• Ostaszewski, K, Glassmeier, K, Goetz, C, Heinisch, P, Henri, P, Park, SA, Ranocha, H, Richter, I, Rubin, M, and Tsurutani, B. 2021. “Steepening of magnetosonic waves in the inner coma of comet 67P/Churyumov-Gerasimenko.” Annales Geophysicae, № 39 (4): 721–742. doi: 10.5194/angeo-39-721-2021.

2020

• Abgrall, R, Mélédo, El, Öffner, P, and Ranocha, H. 2020. “Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes.” in Hyperbolic Problems: Theory, Numerics, Applications, Vol. 10 of AIMS on Applied Mathematics, edited by A Bressan, M Lewicka, D Wang and Y Zheng. Heidelberg: Springer.
• Heinisch, P, Ostaszewski, K, and Ranocha, H. 2020. “Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL.” in Proceedings of the International Workshop on OpenCL, IWOCL '20, April 2020, Munich (Germany) New York, NY: ACM Press. doi: 10.1145/3388333.3403035.
• Ranocha, H. 2020. “Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators.” in Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM} 2018, Vol. 134 of Lecture Notes in Computational Science and Engineering, edited by SJ Sherwin, D Moxey, J Peiró, PE Vincent and C Schwab. Heidelberg: Springer. doi: 10.1007/978-3-030-39647-3_42.
• Ranocha, H, Ostaszewski, K, and Heinisch, P. 2020. “Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators.” Communications on Applied Mathematics and Computation, № 2: 581–611. doi: 10.1007/s42967-019-00057-2.
• Ranocha, H, Sayyari, M, Dalcin, L, Parsani, M, and Ketcheson, DI. 2020. “Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.” SIAM Journal on Scientific Computing, № 42 (2): A612–A638. doi: 10.1137/19M1263480.
• Öffner, P, Glaubitz, J, and Ranocha, H. 2020. “Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods.” International Journal of Numerical Analysis and Modeling, № 17 (3): 332–349.
• Ranocha, H, and Ketcheson, DI. 2020. “Relaxation Runge-Kutta Methods for Hamiltonian Problems.” Journal of Scientific Computing, № 84 (1) doi: 10.1007/s10915-020-01277-y.
• Ranocha, H, Dalcin, L, and Parsani, M. 2020. “Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.” Computers and Mathematics with Applications, № 80 (5): 1343–1359. doi: 10.1016/j.camwa.2020.06.016.
• Ranocha, H, Lóczi, L, and Ketcheson, DI. 2020. “General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes.” Numerische Mathematik, № 146 doi: 10.1007/s00211-020-01158-4.
• Ketcheson, DI, Parsani, M, Grant, ZJ, Ahmadia, A, and Ranocha, H. 2020. “RK-Opt: A package for the design of numerical ODE solvers.” Journal of Open Source Software, № 5 (54): 2514. doi: 10.21105/joss.02514.
• Ranocha, H, and Ketcheson, DI. 2020. “Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems.” SIAM Journal on Numerical Analysis, № 58 (6): 3382–3405. doi: 10.1137/19M1290346.
• Ketcheson, DI, Ranocha, H, Parsani, M, Waheed, U, and Hadjimichael, Y. 2020. “NodePy: A package for the analysis of numerical ODE solvers.” Journal of Open Source Software, № 5 (55): 2515. doi: 10.21105/joss.02515.

2019

• Ranocha, H. 2019. “Mimetic Properties of Difference Operators: Product and Chain Rules as for Functions of Bounded Variation and Entropy Stability of Second Derivatives.” BIT Numerical Mathematics, № 59 (2): 547–563. doi: 10.1007/s10543-018-0736-7.
• Öffner, P, and Ranocha, H. 2019. “Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients.” Journal of Scientific Computing, № 79 (3): 1572–1607. doi: 10.1007/s10915-018-00902-1.
• Öffner, P, Glaubitz, J, and Ranocha, H. 2019. “Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach.” ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), № 52 (6): 2215–2245. doi: 10.1051/m2an/2018072.
• Ranocha, H. 2019. “Some Notes on Summation by Parts Time Integration Methods.” Results in Applied Mathematics, № 1: 100004. doi: 10.1016/j.rinam.2019.100004.

2018

• Ranocha, H. 2018. “Generalised Summation-by-Parts Operators and Entropy Stability of Numerical Methods for Hyperbolic Balance Laws.” Dissertation thesis, TU Braunschweig.
• Glaubitz, J, Öffner, P, Ranocha, H, and Sonar, T. 2018. “Artificial Viscosity for Correction Procedure via Reconstruction Using Summation-by-Parts Operators.” in Theory, Numerics and Applications of Hyperbolic Problems II, Vol. 237 of Springer Proceedings in Mathematics & Statistics, edited by C Klingenberg and M Westdickenberg. Basel: Springer International Publishing. doi: 10.1007/978-3-319-91548-7_28.
• Öffner, P, Ranocha, H, and Sonar, T. 2018. “Correction Procedure via Reconstruction Using Summation-by-Parts Operators.” in Theory, Numerics and Applications of Hyperbolic Problems II, Vol. 237 of Springer Proceedings in Mathematics & Statistics, edited by C Klingenberg and M Westdickenberg. Basel: Springer International Publishing. doi: 10.1007/978-3-319-91548-7_37.
• Ostaszewski, K, Heinisch, P, and Ranocha, H. 2018. “Advantages and Pitfalls of OpenCL in Computational Physics.” in Proceedings of the International Workshop on OpenCL, IWOCL '18, May 2018, Oxford (United Kingdom) New York, NY: ACM Press. doi: 10.1145/3204919.3204929.
• Ranocha, H, Glaubitz, J, Öffner, P, and Sonar, T. 2018. “Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators.” Applied Numerical Mathematics, № 128: 1–23. doi: 10.1016/j.apnum.2018.01.019.
• Ranocha, H. 2018. “Generalised Summation-by-Parts Operators and Variable Coefficients.” Journal of Computational Physics, № 362: 20–48. doi: 10.1016/j.jcp.2018.02.021.
• Ranocha, H, and Öffner, P. 2018. “L_2 Stability of Explicit Runge-Kutta Schemes.” Journal of Scientific Computing, № 75 (2): 1040–1056. doi: 10.1007/s10915-017-0595-4.
• Ranocha, H. 2018. “Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations.” Journal of Scientific Computing, № 76 (1): 216–242. doi: 10.1007/s10915-017-0618-1.

2017

• Ranocha, H, Öffner, P, and Sonar, T. 2017. “Summation-by-Parts and Correction Procedure via Reconstruction.” in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Vol. 119 of Lecture Notes in Computational Science and Engineering, edited by ML Bittencourt, NA Dumont and JS Hesthaven. Heidelberg: Springer. doi: 10.1007/978-3-319-65870-4_45.
• Ranocha, H. 2017. “Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods.” GEM - International Journal on Geomathematics, № 8 (1): 85–133. doi: 10.1007/s13137-016-0089-9.
• Ranocha, H, Öffner, P, and Sonar, T. 2017. “Extended skew-symmetric form for summation-by-parts operators and varying Jacobians.” Journal of Computational Physics, № 342: 13–28. doi: 10.1016/j.jcp.2017.04.044.

2016

• Ranocha, H, Öffner, P, and Sonar, T. 2016. “Summation-by-parts operators for correction procedure via reconstruction.” Journal of Computational Physics, № 311: 299–328. doi: 10.1016/j.jcp.2016.02.009.

2015

• Koenders, C, Glassmeier, K, Richter, I, Ranocha, H, and Motschmann, U. 2015. “Dynamical features and spatial structures of the plasma interaction region of 67P/Churyumov-Gerasimenko and the solar wind.” Planetary and Space Science, № 105: 101–116. doi: 10.1016/j.pss.2014.11.014.