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.
Accepted in Communications on Applied Mathematics and Computation.
[bibtex]
H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani, D. I. Ketcheson.
Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable
Schemes for the Compressible Euler and Navier-Stokes Equations.
arXiv:1905.09129 [math.NA], 2019.
Accepted in SIAM Journal on Scientific Computing.
[bibtex]
D. Rojas, R. Boukharfane, L. Dalcin, D. C. D. R. Fernández, H. Ranocha,
D. E. Keyes, M. Parsani.
On the robustness and performance of entropy stable discontinuous collocation
methods.
arXiv:1911.10966 [math.NA], 2019.
Submitted.
[bibtex]
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]
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]
H. Ranocha.
On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear
Semibounded Operators.
arXiv:1811.11601 [math.NA], 2018.
Submitted.
[bibtex]
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]
H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar.
Time discretisation and L_{2} stability of polynomial summation-by-parts
schemes with Runge-Kutta methods.
arXiv:1609.02393 [math.NA], 2016.
Submitted.
[bibtex]
Energy Stability of Runge-Kutta Methods and a Relaxation Approach.
Rémi Abgrall Group Internal Seminar,
Zürich (Switzerland), December 2019.
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.
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.