Publications

Preprints

  1. Baumann, L. Einkemmer, L. Klingenberg, C. Kusch, J. An adaptive dynamical low-rank optimizer for solving kinetic parameter identification inverse problems. arXiv:2506.21405.
  2. Einkemmer, L., Kusch J., Schotthöfer, S. Construction of high-order conservative basis-update and Galerkin dynamical low-rank integrators. arXiv:2311.06399.
  3. Ceruti, G. Crouseilles, N. Einkemmer, L. A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit. arXiv:2505.19929.
  4. Dang, T.T. Einkemmer, L. Ostermann, A. An initial-boundary corrected splitting method for diffusion-reaction problems. arXiv:2504.10125.
  5. Caliari, M. Cassini, F. Einkemmer, L. Ostermann, A. On the convergence of split exponential integrators for semilinear parabolic problems. arXiv:2503.16210 .
  6. Nakao, J. Ceruti, G. Einkemmer, L. A Reduced Augmentation Implicit Low-rank (RAIL) integrator for solving three-dimensional diffusion and advection-diffusion equations in the Tucker tensor format. arXiv:2503.04932.
  7. Dang, T.T. Einkemmer, L. Ostermann, A. An initial-corrected splitting approach for convection-diffusion-reaction problems. arXiv:2502.09371.
  8. Baumann, L. Einkemmer, L. Klingenberg, C. Kusch. J. An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem. arXiv:2502.03008.
  9. Einkemmer, L., Mangott, J., Prugger, M. Automatic partitioning for the low-rank integration of stochastic Boolean reaction networks. arXiv:2501.04157.
  10. Dektor, A. & Einkemmer, L. Interpolatory dynamical low-rank approximation for the 3+3d Boltzmann-BGK equation. arXiv:2411.15990.
  11. Baumann, L. Einkemmer, L. Klingenberg, C. Jonas, K. A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation. arXiv:2411.06844.
  12. Einkemmer, L. & Moriggl, A. Kinetic scrape off layer simulations with semi-Lagrangian discontinuous Galerkin schemes. arXiv:2408.11235.
  13. Einkemmer, L., Mangott, J. & Prugger, M. A hierarchical dynamical low-rank algorithm for the stochastic description of large reaction networks. arXiv:2311.15143.
  14. Deka, P. J., Einkemmer, L. & Kissmann, R. (2022). Exponential methods for anisotropic diffusion. arXiv:2211.08953.
  15. Deka, P. J., Tokman, M., & Einkemmer, L. (2022). A comparison of Leja-and Krylov-based iterative schemes for Exponential Integrators. arXiv:2211.08948.

Papers

  1. Einkemmer, L., Kormann, K., Kusch, J., McClarren, R. G., Qiu, J. M. A review of low-rank methods for time-dependent kinetic simulations. J. Comput. Phys. DOI arXiv:2412.05912.
  2. Einkemmer, L. Hu, J. Zhang, S. Asymptotic-Preserving Dynamical Low-Rank Method for the Stiff Nonlinear Boltzmann Equation. J. Comput. Phys. DOI arXiv:2502.08951.
  3. Scalone, C. Einkemmer, L. Kusch, J. McClarren, R.J. (2025) A multi-fidelity adaptive dynamical low-rank based optimization algorithm for fission criticality problems. J. Sci. Comput. DOI arXiv:2409.14938.
  4. Einkemmer, L. Hoang, T.-H. Ostermann, A. Should exponential integrators be used for advection-dominated problems? Adv. Appl. Math. Mech. arXiv:2410.12765.
  5. Nakao J., Qiu J.-M. & Einkemmer, L. (2025) Reduced Augmentation Implicit Low-rank (RAIL) integrators for advection-diffusion and Fokker-Planck models. SIAM J. Sci. Comput. DOI arXiv:2311.15143.
  6. Einkemmer, L., Li, Q., Mouhot C. & Yue, Y. (2025) Control of Instability in a Vlasov-Poisson System Through an External Electric Field. J. Comput. Phys. 530, 113904 DOI arXiv:2407.15008.
  7. Einkemmer, L. (2024) Stabilization of beam heated plasmas by beam modulation. Phys. Plasmas 31, 122111 DOI arXiv:2408.16888.
  8. Ceruti G., Einkemmer, L., Kusch J. & Lubich C. (2024) A robust second-order low-rank BUG integrator based on the midpoint rule. BIT Numer. Math 64, 30 DOI arXiv:2402.08607.
  9. Deka, P.J., Moriggl, A. & Einkemmer, L. (2025). LeXInt: GPU-accelerated Exponential Integrators package. SoftwareX 29, 101949 DOI arXiv:2310.08344.
  10. Baumann, L., Einkemmer, L., Klingenberg C. & Kusch, J. (2024). Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem. SIAM J. Sci. Comput. 46:2 DOI arXiv:2307.07538.
  11. Einkemmer, L., Mangott, J. & Prugger, M. (2024). A low-rank complexity reduction algorithm for the high-dimensional kinetic chemical master equation. J. Comput. Phys. 503, 112827 DOI arXiv:2309.08252.
  12. Einkemmer, L. (2024). Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation. J. Comput. Phys. 501, 112757 DOI arXiv:2306.17526.
  13. Deka, P. J., Kissmann, R. & Einkemmer, L. (2024). Efficient numerical methods for Anisotropic Diffusion of Galactic Cosmic Rays. PoS 38th International Cosmic Ray Conference (ICRC2023) 444 DOI arXiv: 2307.12276.
  14. Einkemmer, L. & Moriggl, A. (2024). A semi-Lagrangian discontinuous Galerkin method for drift-kinetic simulations on massively parallel systems. SIAM J. Sci. Comput. 46:2 DOI arXiv:2212.03036.
  15. Einkemmer, L., Li, Q., Wang, L., Yang Y. (2024). Suppressing instability in a Vlasov-Poisson system by an external electric field through constrained optimization. J. Comput. Phys. 498, 112662 DOI arXiv:2305.17994.
  16. Caliari, M., Cassini, F., Einkemmer, L. & Ostermann, A. (2024). Accelerating exponential integrators to efficiently solve advection-diffusion-reaction equations. SIAM J. Sci. Comput. 46:2 DOI arXiv:2303.15861.
  17. Einkemmer, L., Hu, J., & Kusch, J. (2024). Asymptotic-preserving and energy stable dynamical low-rank approximation. SIAM J. Numer. Anal. 62:1 DOI arXiv:2212.12012.
  18. Prugger, M., Einkemmer, L., & Lopez, C. F. (2023). A dynamical low-rank approach to solve the chemical master equation for biological reaction networks. J. Comput. Phys. 489, 112250 DOI bioRxiv.
  19. Einkemmer, L., Ostermann, A., & Scalone, C. (2023). A robust and conservative dynamical low-rank algorithm. J. Comput. Phys. 484, 112060 DOI arXiv:2206.09374
  20. Kusch, J., Einkemmer, L., & Ceruti, G. (2023). On the stability of robust dynamical low-rank approximations for hyperbolic problems. SIAM J. Sci. Comput. 45:1 DOI arXiv:2107.07282
  21. 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. 37:2 DOI arXiv:2110.14557
  22. Deka, P. J., Einkemmer, L., & Tokman, M. (2022). LeXInt: Package for Exponential Integrators employing Leja interpolation. SoftwareX 21, 101302 DOI arXiv:2208.08269
  23. Cassini, F., & Einkemmer, L. (2022). Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign. Comput. Phys. Commun., 280, 108489. DOI arXiv:2110.13481
  24. Deka, P. J., & Einkemmer, L. (2022). Efficient adaptive step size control for exponential integrators. Comput. Math. Appl. 123:1, 59-74 DOI arXiv:2102.02524
  25. Deka, P., & Einkemmer, L. (2022). Exponential Integrators for Resistive Magnetohydrodynamics: Matrix-free Leja interpolation and efficient adaptive time stepping. Astrophys. J., Suppl. Ser., 259:2 DOI arXiv:2108.13622
  26. Kusch, J., Ceruti, G., Einkemmer, L., & Frank, M. (2022). Dynamical low-rank approximation for Burgers’ equation with uncertainty. Int. J. Uncertain. Quantif. 12:5, 1-21 DOI arXiv:2105.04358
  27. Caliari, M., Cassini, F., Einkemmer, L., Ostermann, A., & Zivcovich, F. (2022). A mu-mode integrator for solving evolution equations in Kronecker form. J. Comput. Phys., 455, 110989. DOI arXiv:2103.01691
  28. Einkemmer, L., Ostermann, A., & Residori, M. (2022). A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions. Numer. Math., 150, 105–135. DOI arXiv:2006.05170
  29. Einkemmer, L., Hu, J., & Ying, L. (2022). An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime. SIAM J. Sci. Comput., 43:5, B1057–B1080. DOI arXiv:2101.07104
  30. Einkemmer, L., & Joseph, I. (2021). A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation. J. Comput. Phys., 443, 110495. DOI arXiv
  31. Einkemmer, L., Ostermann, A., & Residori, M. (2021). An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware. Comput. Phys. Commun., 269, 108133. DOI arXiv:2103.06080
  32. Ding, Z., Einkemmer, L., & Li, Q. (2021). Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit. SIAM J. Numer. Anal., 59:4. DOI arXiv:1907.04247
  33. Prugger, M., Einkemmer, L., Beik, S. P., Harris, L. A., & Lopez, C. F. (2021). Unsupervised logic-based mechanism inference for network-driven biological processes. PLOS Comput. Biol., 17:6, e1009035. DOI bioRxiv
  34. Einkemmer, L., Hu, J., & Wang, Y. (2021). An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation. J. Comput. Phys., 439, 110353. DOI arXiv
  35. Caliari, M., Einkemmer, L., Moriggl, A., & Ostermann, A. (2021). An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs. J. Comput. Phys., 437, 110289. DOI arXiv
  36. Einkemmer, L., Ostermann, A., & Residori, M. (2021). A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions. J. Comput. Appl. Math., 385, 113240. DOI arXiv
  37. Crouseilles, N., Einkemmer, L., & Josselin, M. (2020). Exponential methods for solving hyperbolic problems with application to kinetic equations. J. Comput. Phys., 420, 109688. DOI arXiv
  38. Einkemmer, L. (2020). Semi-Lagrangian Vlasov simulation on GPUs. Comput. Phys. Commun., 254, 107351. DOI arXiv
  39. Einkemmer, L., Ostermann, A., & Piazzola, C. (2020). A low-rank projector-splitting integrator for the Vlasov–Maxwell equations with divergence correction. J. Comput. Phys., 403, 109063. DOI arXiv
  40. Einkemmer, L. (2019). Recent advances in structure preserving dynamical low-rank algorithms. Oberwolfach Reports, No. 17/2021. MFO.
  41. Einkemmer, L. (2019). A low-rank algorithm for weakly compressible flow. SIAM J. Sci. Comput., 41(5), A2795–A2814. DOI arXiv
  42. Einkemmer, L., & Lubich, C. (2019). A quasi-conservative dynamical low-rank algorithm for the Vlasov equation. SIAM J. Sci. Comput., 41(5), B1061–B1081. DOI arXiv
  43. Lagravière, J., Langguth, J., Prugger, M., Einkemmer, L., Ha, P. H., & Cai, X. (2019). Performance Optimization and Modeling of Fine-Grained Irregular Communication in UPC. Scientific Programming, 6825728. DOI
  44. Einkemmer, L. (2019). Low-rank approximation of the Boltzmann equation with applications to fluid flow. Oberwolfach Reports, No. 5/2019. MFO.
  45. Wiesenberger, M., Einkemmer, L., Held, M., Gutierrez-Milla, A., Saez, X., & Iakymchuk, R. (2019). Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures. Comput. Phys. Commun., 238, 145–156. DOI arXiv
  46. Einkemmer, L. (2019). A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions. J. Comput. Phys., 376, 937–951. DOI arXiv
  47. Einkemmer, L., & Lubich, C. (2018). A Low-Rank Projector-Splitting Integrator for the Vlasov–Poisson Equation. SIAM J. Sci. Comput., 40, B1330–B1360. DOI arXiv
  48. Wiesenberger, M., Held, M., Einkemmer, L., & Kendl, A. (2018). Streamline integration as a method for structured grid generation in X-point geometry. J. Comput. Phys., 373, 370–384. DOI arXiv
  49. Einkemmer, L. (2018). An adaptive step size controller for iterative implicit methods. Appl. Numer. Math., 132, 182–204. DOI arXiv
  50. Einkemmer, L., & Ostermann, A. (2018). A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev–Petviashvili equation. Appl. Math. Comput., 334, 311–325. DOI arXiv
  51. Einkemmer, L., Moccaldi, M., & Ostermann, A. (2018). Efficient boundary corrected Strang splitting. Appl. Math. Comput., 332, 76–89. DOI arXiv
  52. Auer, N., Einkemmer, L., Kandolf, P., & Ostermann, A. (2018). Magnus integrators on multicore CPUs and GPUs. Comput. Phys. Commun., 228, 115–122. DOI arXiv
  53. Crouseilles, N., Einkemmer, L., & Prugger, M. (2018). An exponential integrator for the drift-kinetic model. Computer Physics Communications, 224, 144–153. DOI arXiv
  54. L. Einkemmer and A. Ostermann. (2017). A comparison of boundary correction methods for Strang splitting. Discrete Contin. Dyn. Syst. Ser. B, 22, 1. DOI arXiv
  55. Einkemmer, L. (2017). Evaluation of the Intel Xeon Phi and NVIDIA K80 as accelerators for two-dimensional panel codes. PLoS ONE. DOI arXiv
  56. Wiesenberger, M., Held, M., & Einkemmer, L. (2017). Streamline integration as a method for two-dimensional elliptic grid generation. J. Comput. Phys., 340, 435–450. DOI arXiv
  57. Gasteiger, M., Einkemmer, L., Ostermann, A., & Tskhakaya, D. (2017). Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation. J. Plasma Phys., 83(1), 705830107. DOI arXiv
  58. Einkemmer, L. (2017). A study on conserving invariants of the Vlasov equation in semi-Lagrangian computer simulations. J. Plasma Phys., 83(2), 705830203. DOI arXiv
  59. Einkemmer, L., Tokman, M., & Loffeld, J. (2016). On the performance of exponential integrators for problems in magnetohydrodynamics. J. Comput. Phys., 330, 550–565. DOI arXiv
  60. Prugger, M., Einkemmer, L., & Ostermann, A. (2016). Evaluation of the Partitioned Global Address Space (PGAS) model for an inviscid Euler solver. Parallel Comput., 60, 22–40. DOI arXiv
  61. Einkemmer, L., & Ostermann, A. (2016). Overcoming order reduction in diffusion-reaction splitting. Part 2: oblique boundary conditions. SIAM J. Sci. Comput., 38(6), A3741–A3757. DOI arXiv
  62. Crouseilles, N., Einkemmer, L., & Faou, E. (2016). An asymptotic preserving scheme for the relativistic Vlasov–Maxwell equations in the classical limit. Comput. Phys. Commun., 209, 13–26. DOI arXiv
  63. Einkemmer, L. (2016). Structure preserving numerical methods for the Vlasov equation. Oberwolfach Reports, No. 18/2016. MFO.
  64. Einkemmer, L. (2016). A mixed precision semi-Lagrangian algorithm and its performance on accelerators. High Performance Computing and Simulation (HPCS), International Conference On. DOI arXiv
  65. Einkemmer, L. (2016). High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code. Comput. Phys. Commun., 202, 326–336. DOI arXiv
  66. Einkemmer, L. (2016). A modern resistive magnetohydrodynamics solver using C++ and the Boost library. Comput. Phys. Commun., 206, 69–77. DOI arXiv
  67. Einkemmer, L., & Ostermann, A. (2015). A splitting approach for the Kadomtsev–Petviashvili equation. J. Comput. Phys., 299, 716–730. DOI arXiv
  68. Einkemmer, L., & Ostermann, A. (2015). Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions. SIAM J. Sci. Comput., 37(3), A1577–A1592. DOI arXiv
  69. Einkemmer, L., Vörös, Z., Weihs, G., & Portolan, S. (2015). Polarization entanglement generation in microcavity polariton devices. Phys. Status Solidi (b)., 252(8), 1749–1756. DOI arXiv
  70. Einkemmer, L., & Ostermann, A. (2015). On the error propagation of semi-Lagrange and Fourier methods for advection problems. Comput. Math. Appl., 69(3), 170–179. DOI arXiv
  71. Crouseilles, N., Einkemmer, L., & Faou, E. (2015). A Hamiltonian splitting for the Vlasov–Maxwell system. J. Comput. Phys., 238, 224–240. DOI arXiv
  72. Einkemmer, L., & Wiesenberger, M. (2014). A conservative discontinuous Galerkin scheme for the 2D incompressible Navier–Stokes equations. Comput. Phys. Commun., 185(11), 2865–2873. DOI arXiv
  73. Einkemmer, L., & Ostermann, A. (2014). A comparison of triple jump and Suzuki fractals for obtaining high order from an almost symmetric Strang splitting scheme. Oberwolfach Reports, No. 14/2014. MFO.
  74. Einkemmer, L., & Ostermann, A. (2014). A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D, 68, 197. DOI arXiv
  75. Portolan, S., Einkemmer, L., Vörös, Z., Weihs, G., & Rabl, P. (2014). Generation of hyper-entangled photon pairs in coupled microcavities. New J. Phys., 16, 063030. DOI arXiv
  76. Einkemmer, L., & Ostermann, A. (2014). An almost symmetric Strang splitting scheme for the construction of high order composition methods. Comput. Appl. Math., 271, 307–318. DOI arXiv
  77. Einkemmer, L., & Ostermann, A. (2014). An almost symmetric Strang splitting scheme for nonlinear evolution equations. Comput. Math. Appl., 67(12), 2144–2157. DOI arXiv
  78. Einkemmer, L., & Ostermann, A. (2014). Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov–Poisson equations. SIAM J. Numer. Anal., 52(2), 757–778. DOI arXiv
  79. Einkemmer, L., & Ostermann, A. (2014). Convergence analysis of Strang splitting for Vlasov-type equations. SIAM J. Numer. Anal., 52(1), 140–155. DOI arXiv
  80. Einkemmer, L., & Ostermann, A. (2013). Exponential integrators on graphic processing units. High Performance Computing and Simulation (HPCS), International Conference On. DOI arXiv

Book chapter

L. Einkemmer, A. Ostermann (editors M. Barden, A. Ostermann)
Scientific Computing @ uibk
Innsbruck University Press

PhD thesis

Splitting methods for the Vlasov-Poisson and Vlasov-Maxwell equations (pdf)
Advisor: Alexander Ostermann

Master theses

Parametric scattering in microcavities (pdf)
Advisor: Gregor Weihs, Zoltán Vörös

Exponential integrators on graphic processing units (pdf)
Advisor: Alexander Ostermann

Bachelor theses

Monte Carlo methods (pdf)
Advisor: Alexander Ostermann

Topics in non-linear differential equations (pdf)
Advisor: Norbert Ortner

HTL final project (german)

BioAuth - Ein System zur biometrischen Authentifizierung
Advisor: Michael Weiss

Term papers

Quasi-Monte Carlo methods (pdf)