90 citations · 1k across the 88 of their papers we have counts for
7 papers · 2 filters
Reduced Augmentation Implicit Low-rank (RAIL) integrators for advection-diffusion and Fokker-Planck models
Joseph Nakao, Jing-Mei Qiu, Lukas Einkemmer
This paper introduces a novel computational approach termed the Reduced Augmentation Implicit Low-rank (RAIL) method by investigating two predominant research directions in low-ran…
Construction of high-order conservative basis-update and Galerkin dynamical low-rank integrators
Lukas Einkemmer, Jonas Kusch, Steffen Schotthöfer
Numerical simulations of kinetic problems can become prohibitively expensive due to their large memory requirements and computational costs. A method that has proven to successfull…
LeXInt: GPU-accelerated Exponential Integrators package
Pranab J Deka, Alexander Moriggl, Lukas Einkemmer
We present an open-source CUDA-based package that consists of a compilation of exponential integrators where the action of the matrix exponential or the functions on a vector…
A low-rank complexity reduction algorithm for the high-dimensional kinetic chemical master equation
Lukas Einkemmer, Julian Mangott, Martina Prugger
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the ch…
Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finel…
Suppressing Instability in a Vlasov-Poisson System by an External Electric Field Through Constrained Optimization
Lukas Einkemmer, Qin Li, Li Wang +1
Fusion energy offers the potential for the generation of clean, safe, and nearly inexhaustible energy. While notable progress has been made in recent years, significant challenges…
Accelerating exponential integrators to efficiently solve semilinear advection-diffusion-reaction equations
Marco Caliari, Fabio Cassini, Lukas Einkemmer +1
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually m…