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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
  • 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
    • Heterogeneous computing on CPUs and GPUs using OpenCL
    • Open source projects such as Trixi.jl, OrdinaryDiffEq.jl, NodePy, RK-Opt

News

New Paper ‘Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts’ published in Journal of Scientific Computing 2021-04-07

New Paper ‘A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions’ published in Journal of Scientific Computing 2021-03-11

New Paper ‘A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations’ published in Communications in Computational Physics 2021-03-07

New Paper ‘On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations’ on arXiv 2021-01-16

New Preprint ‘Steepening of magnetosonic waves in the inner coma of comet 67P/Churyumov-Gerasimenko’ 2020-12-20