Publications

Preprints

  1. Einkemmer, L., Ostermann, A., & Scalone, C. (2022). A robust and conservative dynamical low-rank algorithm. arXiv:2206.09374.
  2. Prugger, M., Einkemmer, L., & Lopez, C. F. (2022). A dynamical low-rank approach to solve the chemical master equation for biological reaction networks. bioRxiv.
  3. Cassini, F., & Einkemmer, L. (2021). Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign. arXiv:2110.13481.
  4. Einkemmer, L., & Alexander, M. (2021). Semi-Lagrangian 4d, 5d, and 6d kinetic plasma simulation on large scale GPU equipped supercomputer. arXiv:2110.14557.
  5. Kusch, J., Einkemmer, L., & Ceruti, G. (2021). On the stability of robust dynamical low-rank approximations for hyperbolic problems. arXiv:2107.07282.

Papers

  1. Deka, P. J., & Einkemmer, L. (2022). Efficient adaptive step size control for exponential integrators. To Appear in Comput. Math. Appl. DOI arXiv:2102.02524
  2. Deka, P., & Einkemmer, L. (2022). Exponential Integrators for MHD: Matrix-free Leja interpolation and efficient adaptive time stepping. Astrophys. J., Suppl. Ser., 259(2). DOI arXiv:2108.13622
  3. Kusch, J., Ceruti, G., Einkemmer, L., & Frank, M. (2022). Dynamical low-rank approximation for Burgers’ equation with uncertainty. Int. J. Uncertain. Quantif. DOI arXiv:2105.04358
  4. Caliari, M., Cassini, F., Einkemmer, L., Ostermann, A., & Zivcovich, F. (2022). A mu-mode integrator for solving evolution equations in Kronecker form. J. Comp. Phys., 455, 110989. DOI arXiv:2103.01691
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. Einkemmer, L. (2020). Semi-Lagrangian Vlasov simulation on GPUs. Comput. Phys. Commun., 254, 107351. DOI arXiv
  16. 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
  17. Einkemmer, L. (2019). Recent advances in structure preserving dynamical low-rank algorithms. Oberwolfach Reports, No. 17/2021. MFO.
  18. Einkemmer, L. (2019). A low-rank algorithm for weakly compressible flow. SIAM J. Sci. Comput., 41(5), A2795–A2814. DOI arXiv
  19. 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
  20. 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
  21. Einkemmer, L. (2019). Low-rank approximation of the Boltzmann equation with applications to fluid flow. Oberwolfach Reports, No. 5/2019. MFO.
  22. 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
  23. 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
  24. 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
  25. 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
  26. Einkemmer, L. (2018). An adaptive step size controller for iterative implicit methods. Appl. Numer. Math., 132, 182–204. DOI arXiv
  27. 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
  28. Einkemmer, L., Moccaldi, M., & Ostermann, A. (2018). Efficient boundary corrected Strang splitting. Appl. Math. Comput., 332, 76–89. DOI arXiv
  29. Auer, N., Einkemmer, L., Kandolf, P., & Ostermann, A. (2018). Magnus integrators on multicore CPUs and GPUs. Comput. Phys. Commun., 228, 115–122. DOI arXiv
  30. Crouseilles, N., Einkemmer, L., & Prugger, M. (2018). An exponential integrator for the drift-kinetic model. Computer Physics Communications, 224, 144–153. DOI arXiv
  31. 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
  32. Einkemmer, L. (2017). Evaluation of the Intel Xeon Phi and NVIDIA K80 as accelerators for two-dimensional panel codes. PLoS ONE. DOI arXiv
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. Einkemmer, L. (2016). Structure preserving numerical methods for the Vlasov equation. Oberwolfach Reports, No. 18/2016. MFO.
  41. 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
  42. Einkemmer, L. (2016). High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code. Comput. Phys. Commun., 202, 326–336. DOI arXiv
  43. Einkemmer, L. (2016). A modern resistive magnetohydrodynamics solver using C++ and the Boost library. Comput. Phys. Commun., 206, 69–77. DOI arXiv
  44. Einkemmer, L., & Ostermann, A. (2015). A splitting approach for the Kadomtsev–Petviashvili equation. J. Comput. Phys., 299, 716–730. DOI arXiv
  45. 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
  46. 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
  47. 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
  48. Crouseilles, N., Einkemmer, L., & Faou, E. (2015). A Hamiltonian splitting for the Vlasov–Maxwell system. J. Comput. Phys., 238, 224–240. DOI arXiv
  49. 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
  50. 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.
  51. Einkemmer, L., & Ostermann, A. (2014). A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D, 68, 197. DOI arXiv
  52. 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
  53. 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
  54. Einkemmer, L., & Ostermann, A. (2014). An almost symmetric Strang splitting scheme for nonlinear evolution equations. Comput. Math. Appl., 67(12), 2144–2157. DOI arXiv
  55. 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
  56. Einkemmer, L., & Ostermann, A. (2014). Convergence analysis of Strang splitting for Vlasov-type equations. SIAM J. Numer. Anal., 52(1), 140–155. DOI arXiv
  57. 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)