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Hendrik Ranocha is a Postdoctoral Fellow in the Cluster of Excellence at the University of Münster, Germany.

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 as well as mimetic and 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, continuous and discontinuous spectral element 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
    • Adaptivity in time and space
    • Data-driven approaches combining analysis and data
  • Scientific Computing
    • Compressible Euler equations, shallow water equations, magnetic induction equation, numerical plasma physics, magnetohydrodynamics, dispersive wave equations
    • Multi-physics problems and astrophysical applications
    • Modeling and analysis of physical processes
    • High-performance computing (HPC) in Julia
    • Heterogeneous computing on CPUs and GPUs using OpenCL
    • Open source projects such as Trixi.jl, SummationByPartsOperators.jl, OrdinaryDiffEq.jl, NodePy, RK-Opt

Brief CV

  • 2021/03–present: Postdoctoral Fellow, University of Münster (Germany). Advisor: Mario Ohlberger
  • 2019/09–2021/02: Postdoctoral Fellow, King Abdullah University of Science and Technology (KAUST, Saudi Arabia). Advisor: David Ketcheson
  • 2018/02–2019/09: Postdoctoral Research and Teaching Associate, TU Braunschweig (Germany) Advisor: Thomas Sonar
  • 2018/03–2019/02: Teaching assignment, Ostfalia University of Applied Sciences (Germany)
  • 2016/04–2018/02: PhD Mathematics, TU Braunschweig (Germany). Advisor: Thomas Sonar
  • 2014/10–2016/02: MSc Mathematics, TU Braunschweig (Germany)
  • 2011/10–2014/09: BSc Mathematics, TU Braunschweig (Germany)
  • 2013/08–2013/12: Exchange student, Yonsei University (Seoul, South Korea)
  • 2010/10–2013/07: BSc Physics, TU Braunschweig (Germany)

News

New Paper ‘On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations’ published in Partial Differential Equations and Applications 2021-10-18

New Paper ‘SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties’ published in the Journal of Open Source Software 2021-08-25

New Preprint ‘A New Stability Approach for Positivity-Preserving Patankar-type Schemes’ on arXiv 2021-08-18

New Preprint ‘Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing’ on arXiv 2021-08-17

New Paper ‘Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes’ published in Communications on Applied Mathematics and Computation 2021-08-02