Publications
Preprints
- Prugger, M., Einkemmer, L., & Lopez, C. F. (2022). A dynamical low-rank approach to solve the chemical master equation for biological reaction networks. bioRxiv.
- Cassini, F., & Einkemmer, L. (2021). Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign. arXiv:2110.13481.
- Einkemmer, L., & Alexander, M. (2021). Semi-Lagrangian 4d, 5d, and 6d kinetic plasma simulation on large scale GPU equipped supercomputer. arXiv:2110.14557.
- Kusch, J., Einkemmer, L., & Ceruti, G. (2021). On the stability of robust dynamical low-rank approximations for hyperbolic problems. arXiv:2107.07282.
- Deka, P. J., & Einkemmer, L. (2021). Efficient adaptive step size control for exponential integrators. arXiv:2102.02524.
Papers
- 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
- Kusch, J., Ceruti, G., Einkemmer, L., & Frank, M. (2022). Dynamical low-rank approximation for Burgers’ equation with uncertainty. To Appear in Int. J. Uncertain. Quantif. DOI arXiv:2105.04358
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Einkemmer, L. (2020). Semi-Lagrangian Vlasov simulation on GPUs. Comput. Phys. Commun., 254, 107351. DOI arXiv
- 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
- Einkemmer, L. (2019). Recent advances in structure preserving dynamical low-rank algorithms. Oberwolfach Reports, No. 17/2021. MFO.
- Einkemmer, L. (2019). A low-rank algorithm for weakly compressible flow. SIAM J. Sci. Comput., 41(5), A2795–A2814. DOI arXiv
- 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
- 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
- Einkemmer, L. (2019). Low-rank approximation of the Boltzmann equation with applications to fluid flow. Oberwolfach Reports, No. 5/2019. MFO.
- 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
- 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
- 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
- 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
- Einkemmer, L. (2018). An adaptive step size controller for iterative implicit methods. Appl. Numer. Math., 132, 182–204. DOI arXiv
- 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
- Einkemmer, L., Moccaldi, M., & Ostermann, A. (2018). Efficient boundary corrected Strang splitting. Appl. Math. Comput., 332, 76–89. DOI arXiv
- Auer, N., Einkemmer, L., Kandolf, P., & Ostermann, A. (2018). Magnus integrators on multicore CPUs and GPUs. Comput. Phys. Commun., 228, 115–122. DOI arXiv
- Crouseilles, N., Einkemmer, L., & Prugger, M. (2018). An exponential integrator for the drift-kinetic model. Computer Physics Communications, 224, 144–153. DOI arXiv
- 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
- Einkemmer, L. (2017). Evaluation of the Intel Xeon Phi and NVIDIA K80 as accelerators for two-dimensional panel codes. PLoS ONE. DOI arXiv
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Einkemmer, L. (2016). Structure preserving numerical methods for the Vlasov equation. Oberwolfach Reports, No. 18/2016. MFO.
- 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
- Einkemmer, L. (2016). High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code. Comput. Phys. Commun., 202, 326–336. DOI arXiv
- Einkemmer, L. (2016). A modern resistive magnetohydrodynamics solver using C++ and the Boost library. Comput. Phys. Commun., 206, 69–77. DOI arXiv
- Einkemmer, L., & Ostermann, A. (2015). A splitting approach for the Kadomtsev–Petviashvili equation. J. Comput. Phys., 299, 716–730. DOI arXiv
- 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
- 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
- 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
- Crouseilles, N., Einkemmer, L., & Faou, E. (2015). A Hamiltonian splitting for the Vlasov–Maxwell system. J. Comput. Phys., 238, 224–240. DOI arXiv
- 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
- 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.
- Einkemmer, L., & Ostermann, A. (2014). A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D, 68, 197. DOI arXiv
- 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
- 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
- Einkemmer, L., & Ostermann, A. (2014). An almost symmetric Strang splitting scheme for nonlinear evolution equations. Comput. Math. Appl., 67(12), 2144–2157. DOI arXiv
- 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
- Einkemmer, L., & Ostermann, A. (2014). Convergence analysis of Strang splitting for Vlasov-type equations. SIAM J. Numer. Anal., 52(1), 140–155. DOI arXiv
- 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)