I am an Assistant Professor in Applied Mathematics at the University of Hamburg. 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.
- 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.
New Paper ‘On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics’ published in Communications on Applied Mathematics and Computation 2023-05-22
Tutorial on the Julia programming language and Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic PDEs on 2023-05-24 2023-05-16
Talk ‘Structure-preserving numerical methods for dispersive wave equations’ on 2023-05-31 2023-05-10
New Preprint ‘Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biology and numerical methods for ODEs’ on arXiv 2023-04-06
New Preprint ‘Resolving Entropy Growth from Iterative Methods’ on arXiv 2023-02-28