Publications

Journals

  1. H. Ranocha. Some Notes on Summation by Parts Time Integration Methods. Results in Applied Mathematics, 1: 100004, 2019. arXiv:1901.08377 [math.NA]. [bibtex]
  2. P. Öffner, J. Glaubitz, H. Ranocha. 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, 2019. arXiv:1703.03561 [math.NA]. [bibtex]
  3. P. Öffner, H. Ranocha. Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients. Journal of Scientific Computing, 79.3: 1572-1607, 2019. arXiv:1806.02018 [math.NA]. [bibtex]
    A full-text view-only version is available at https://rdcu.be/bfNr5.
  4. H. Ranocha. 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, 2019. arXiv:1805.09126 [math.NA]. [bibtex]
    A full-text view-only version is available at https://rdcu.be/baAC2.
  5. H. Ranocha, P. Öffner. L2 Stability of Explicit Runge-Kutta Schemes. Journal of Scientific Computing, 75.2: 1040-1056, 2018. [bibtex]
    A full-text view-only version is available at http://rdcu.be/x6Rl.
  6. H. Ranocha. Generalised Summation-by-Parts Operators and Variable Coefficients. Journal of Computational Physics, 362: 20-48, 2018. arXiv:1705.10541 [math.NA]. [bibtex]
    The full-text is available at https://authors.elsevier.com/a/1Wbh-508HeRTj until 2018-04-12.
  7. H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar. Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators. Applied Numerical Mathematics, 2018. See also arXiv:1606.00995 [math.NA] and arXiv:1606.01056 [math.NA]. [bibtex]
    The full-text is available at https://authors.elsevier.com/a/1WWcX_3rqbu4MC until 2018-03-29.
  8. H. Ranocha. Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations. Journal of Scientific Computing, 76(1): 216-242, 2018. arXiv:1701.02264 [math.NA]. [bibtex]
    A full-text view-only version is available at http://rdcu.be/AefL.
  9. H. Ranocha, P. Öffner, T. Sonar. Extended skew-symmetric form for summation-by-parts operators and varying Jacobians. Journal of Computational Physics, 342: 13-28, 2017. arXiv:1511.08408 [math.NA]. [bibtex]
  10. H. Ranocha. Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods. GEM - International Journal on Geomathematics, 8(1): 85-133, 2017. arXiv:1609.08029 [math.NA]. [bibtex]
  11. H. Ranocha, P. Öffner, T. Sonar. Summation-by-parts operators for correction procedure via reconstruction. Journal of Computational Physics, 311: 299-328, 2016. arXiv:1511.02052 [math.NA]. [bibtex]
  12. C. Koenders, K.-H. Glassmeier, I. Richter, H. Ranocha, U. Motschmann. 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, 2015. [bibtex]

Preprints

  1. H. Ranocha, D. I. Ketcheson. Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems. arXiv:1909.13215 [math.NA], 2019. Submitted. [bibtex]
  2. H. Ranocha, K. Ostaszewski, P. Heinisch. Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators. arXiv:1908.08732 [math.NA], 2019. Submitted. [bibtex]
  3. R. Abgrall, P. Öffner, H. Ranocha. Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes. arXiv:1908.04556 [math.NA], 2019. Submitted. [bibtex]
  4. H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani, D. I. Ketcheson. Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Euler and Navier-Stokes Equations. arXiv:1905.09129 [math.NA], 2019. Submitted. [bibtex]
  5. H. Ranocha. On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators. arXiv:1811.11601 [math.NA], 2018. Submitted. [bibtex]
  6. H. Ranocha, K. Ostaszewski, P. Heinisch. Numerical Methods for the Magnetic Induction Equation with Hall Effect and Projections onto Divergence-Free Vector Fields. arXiv:1810.01397 [math.NA], 2018. Submitted. [bibtex]
  7. H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar. Time discretisation and L2 stability of polynomial summation-by-parts schemes with Runge-Kutta methods. arXiv:1609.02393 [math.NA], 2016. Submitted. [bibtex]

Theses

Talks and Conferences

  • On Strong Stability of Runge-Kutta Methods. Computer, Electrical and Mathematical Sciences and Engineering Seminar, King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia), April 2019.
  • On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Problems. VII European Workshop on High Order Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM), Madrid (Spain), April 2019.
  • High-Order Methods on Summation by Parts Form for the Magnetic Induction Equation. VII European Workshop on High Order Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM), Madrid (Spain), April 2019.
  • Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators. International Conference on Spectral and High Order Methods (ICOSAHOM), London (United Kingdom), July 2018.
  • K. Ostaszewski, P. Heinisch, H. Ranocha. Advantages and Pitfalls of OpenCL in Computational Physics.. Proceedings of the International Workshop on OpenCL. IWOCL '18, May 2018, Oxford (United Kingdom). New York, NY, USA: ACM, 2018, p. 10:1. [bibtex]
  • Generalised Summation-by-Parts Operators, Entropy Stability, and Split Forms. Numerical Analysis Group Internal Seminar, Oxford (United Kingdom), October 2017.
  • J. Glaubitz, P. Öffner, H. Ranocha, T. Sonar. Artificial Viscosity for Correction Procedure via Reconstruction Using Summation-by-Parts Operators.. Theory, Numerics and Applications of Hyperbolic Problems II. Ed. by C. Klingenberg, M. Westdickenberg. Vol. 237. Springer Proceedings in Mathematics & Statistics. Cham: Springer International Publishing, 2018, pp. 363-375. [bibtex]
  • Correction Procedure via Reconstruction Using Summation-by-Parts Operators. International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP), Aachen (Germany), August 2016.
    P. Öffner, H. Ranocha, T. Sonar. Correction Procedure via Reconstruction Using Summation-by-Parts Operators.. Theory, Numerics and Applications of Hyperbolic Problems II. Ed. by C. Klingenberg, M. Westdickenberg. Vol. 237. Springer Proceedings in Mathematics & Statistics. Cham: Springer International Publishing, 2018, pp. 491-501. [bibtex]
  • Summation-by-Parts and Correction Procedure via Reconstruction. International Conference on Spectral and High Order Methods (ICOSAHOM), Rio de Janeiro (Brazil), June 2016.
    H. Ranocha, P. Öffner, T. Sonar. Summation-by-Parts and Correction Procedure via Reconstruction.. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Ed. by M. L. Bittencourt, N. A. Dumont, J. S. Hesthaven. Vol. 119. Lecture Notes in Computational Science and Engineering. Cham: Springer, 2017, pp. 627-637. [bibtex]
  • Correction procedure via reconstruction using summation-by-parts operators. Vincent Lab Internal Seminar, Imperial College London (United Kingdom), April 2016.