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Hendrik Ranocha is a Postdoctoral Fellow in the group of David I. Ketcheson at KAUST (King Abdullah University of Science and Technology, Saudi Arabia).

His research is focused on the analysis and development of numerical methods for partial and ordinary differential equations. In particular, he is interested in the stability of these schemes and mimetic & structure-preserving techniques, allowing the transfer of results from the continuous level to the discrete one.

Research Interests

• Numerical Analysis
  • Numerical schemes for hyperbolic balance laws and dispersive-dissipative equations: Discontinuous Galerkin methods, finite difference schemes, flux reconstruction, finite volume methods
  • Structure-preserving methods: Conservation/dissipation of entropy/energy, summation by parts operators, (skew-symmetric) splitting techniques, mimetic properties, filtering, artificial dissipation
  • Runge-Kutta methods, stability of time integration schemes
• Scientific Computing
  • Compressible Euler equations, shallow water equations, magnetic induction equation, numerical plasma physics, magnetohydrodynamics, dispersive wave equations
  • Modeling and analysis of physical processes
  • Heterogeneous computing on CPUs and GPUs using OpenCL

News

New Paper ‘A conservative fully-discrete numerical method for the regularised shallow water wave equations’ on arXiv 2020-09-22

New Paper ‘A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics’ on arXiv 2020-08-25

Conference Proceedings ‘Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators’ of ICOSAHOM 2018 published 2020-08-16

New Paper ‘Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts’ on arXiv 2020-07-17

New Paper ‘Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations’ published in Computers and Mathematics with Applications 2020-07-12