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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.

News

New Paper ‘On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws’ published in the Journal of Computational Physics 2024-10-10

Arpit presents his work at the Indo-german Workshop on Hardware-aware Scientific Computing (IGHASC) 2024-10-10

Mathematics of the Weather 2024 conference with several contributions 2024-09-30

Marco Artiano has published his first paper ‘On the Performances of Standard and Kinetic Energy Preserving Time-Integration Methods for Incompressible-Flow Simulations’ in Flow, Turbulence and Combustion 2024-09-29

New Paper ‘Stability of step size control based on a posteriori error estimates’ published in Computational Science and Engineering 2024-09-24