90 citations · 1k across the 88 of their papers we have counts for
6 papers · 1 filter
Asymptotic--preserving and energy stable dynamical low-rank approximation
Lukas Einkemmer, Jingwei Hu, Jonas Kusch
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computat…
Exponential methods for anisotropic diffusion
Pranab J. Deka, Lukas Einkemmer, Ralf Kissmann
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This d…
A semi-Lagrangian discontinuous Galerkin method for drift-kinetic simulations on GPUs
Lukas Einkemmer, Alexander Moriggl
In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In t…
A comparison of Leja- and Krylov-based iterative schemes for Exponential Integrators
Pranab J. Deka, Mayya Tokman, Lukas Einkemmer
Krylov-based algorithms have long been preferred to compute the matrix exponential and exponential-like functions appearing in exponential integrators. Of late, direct polynomial i…
LeXInt: Package for Exponential Integrators employing Leja interpolation
Pranab J. Deka, Lukas Einkemmer, Mayya Tokman
We present a publicly available software for exponential integrators that computes the functions using polynomial interpolation. The interpolation method at Leja points ha…
A robust and conservative dynamical low-rank algorithm
Lukas Einkemmer, Alexander Ostermann, Carmen Scalone
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preser…