Research

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 (external website).