90 citations · 1k across the 88 of their papers we have counts for
8 papers · 2 filters
A review of low-rank methods for time-dependent kinetic simulations
Lukas Einkemmer, Katharina Kormann, Jonas Kusch +2
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised…
Interpolatory dynamical low-rank approximation for the 3+3d Boltzmann-BGK equation
Alec Dektor, Lukas Einkemmer
We introduce two novel interpolatory dynamical low-rank (DLR) approximation methods for the efficient time integration of the Boltzmann-BGK equation. Both methods overcome limitati…
A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort.…
Should exponential integrators be used for advection-dominated problems?
Lukas Einkemmer, Trung-Hau Hoang, Alexander Ostermann
In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context,…
A multi-fidelity adaptive dynamical low-rank based optimization algorithm for fission criticality problems
C. Scalone, L. Einkemmer, J. Kusch +1
Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work…
Kinetic scrape off layer simulations with semi-Lagrangian discontinuous Galerkin schemes
Lukas Einkemmer, Alexander Moriggl
In this paper we propose a semi-Lagrangian discontinuous Galerkin solver for the simulation of the scrape off layer for an electron-ion plasma. We use a time adaptive velocity spac…
A hierarchical dynamical low-rank algorithm for the stochastic description of large reaction networks
Lukas Einkemmer, Julian Mangott, Martina Prugger
The stochastic description of chemical reaction networks with the kinetic chemical master equation (CME) is important for studying biological cells, but it suffers from the curse o…
A robust second-order low-rank BUG integrator based on the midpoint rule
Gianluca Ceruti, Lukas Einkemmer, Jonas Kusch +1
Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly model order reduction for prohibitively large matrix differential equations. A core ingredient…