Research

Explore some of our research

Low-rank complexity reduction for kinetic equations

Algorithms for solving kinetic equations efficiently by reducing them to lower-dimensional evolution equations

Structure preserving numerical methods

Numerical methods that preserve the physical structure of equations (e.g. energy conserving methods)

Plasma physics and magnetic confinement fusion

Suppressing instabilities and efficiently simulating plasma dynamics

High-performance computing

Solving challenging problems on GPUs and supercomputers

Innovative time integrators/avoiding order reduction

Modern time integration methods such as splitting schemes, exponential integrators, IMEX methods, etc.

or look at a list of representative publications.

Selected publications

  1. Einkemmer, L., Kormann, K., Kusch, J., McClarren, R. G., Qiu, J. M. (2025). A review of low-rank methods for time-dependent kinetic simulations. J. Comput. Phys. DOI arXiv.
  2. Einkemmer, L., & Lubich, C. (2018). A Low-Rank Projector-Splitting Integrator for the Vlasov–Poisson Equation. SIAM J. Sci. Comput., DOI arXiv
  3. Crouseilles, N., Einkemmer, L., & Faou, E. (2015). A Hamiltonian splitting for the Vlasov–Maxwell system. J. Comput. Phys., DOI arXiv
  4. Einkemmer, L. (2024). Stabilization of beam heated plasmas by beam modulation. Phys. Plasmas DOI arXiv.
  5. Einkemmer, L., & Moriggl, A. (2022). Semi-Lagrangian 4d, 5d, and 6d kinetic plasma simulation on large scale GPU equipped supercomputer. Int. J. High Perform. Comput. Appl. DOI arXiv
  6. Einkemmer, L., & Ostermann, A. (2015). Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions. SIAM J. Sci. Comput., DOI arXiv
  7. Einkemmer, L., & Joseph, I. (2021). A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation. J. Comput. Phys. DOI arXiv
  8. Dektor, A. & Einkemmer, L. (2026). Interpolatory dynamical low-rank approximation for the 3+3d Boltzmann-BGK equation. J. Comput. Phys. DOI arXiv.
  9. Einkemmer, L., Mangott, J. & Prugger, (2026). M. A hierarchical dynamical low-rank algorithm for the stochastic description of large reaction networks. SIAM J. Sci. Comput. arXiv:2311.15143.
  10. Einkemmer, L., & Ostermann, A. (2014). Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov–Poisson equations. SIAM J. Numer. Anal. DOI arXiv