arXiv.orgHome
I am a Professor in Numerical Mathematics at Johannes Gutenberg University Mainz. My research is focused on the analysis and development of numerical methods for partial and ordinary differential equations. In particular, I am 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
- Uncertainty quantification
- 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
Please find more information about our research in the section Research.
CV and members of the research group
Please find more information about us in the section People.