90 citations · 1k across the 88 of their papers we have counts for
71 papers · 1 filter
Low-rank SI-DSA and GMRES-DSA for Radiative Transfer Equation with Adaptive Accuracy Control
Chenxi Han, Lukas Einkemmer, Wei Guo +1
Recently, efficient sweep-based low-rank iterative solvers have been developed to reduce the computational costs of steady-state solves and implicit time integration of the radiati…
A Memory-Efficient Adjoint State Optimization Method Based on Time-Reversible Dynamical Low-Rank Approximation
Lukas Einkemmer, Julian Mangott
The primary challenge of conducting PDE-constrained optimization for high-dimensional problems, such as kinetic equations, is the often prohibitive memory cost. Computing gradients…
Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations
Stefan Brunner, Lukas Einkemmer, Terry Haut
In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a…
Efficient SN-like and PN-like Dynamic Low Rank methods for Thermal Radiative Transfer
Terry Haut, John Loffeld, Lukas Einkemmer +3
Dynamic Low Rank (DLR) methods are a promising way to reduce the computational cost and memory footprint of the high-dimensional thermal radiative transfer (TRT) equations. The TRT…
A simple predictor-corrector scheme without order reduction for advection-diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Treating diffusion and advection/reaction separately is an effective strategy for solving semilinear advection-diffusion-reaction equations. However, such an approach is prone to s…
An adaptive dynamical low-rank optimizer for solving kinetic parameter identification problems
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
The numerical solution of parameter identification problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank sc…
A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit
Gianluca Ceruti, Nicolas Crouseilles, Lukas Einkemmer
The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work,…
An initial-boundary corrected splitting method for diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order for Dirichlet boundary c…
On the convergence of split exponential integrators for semilinear parabolic problems
Marco Caliari, Fabio Cassini, Lukas Einkemmer +1
Splitting the exponential-like functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational…
A low-rank, high-order implicit-explicit integrator for three-dimensional convection-diffusion equations
Joseph Nakao, Gianluca Ceruti, Lukas Einkemmer
This paper presents a rank-adaptive implicit-explicit integrator for the tensor approximation of three-dimensional convection-diffusion equations. In particular, the recently devel…
An initial-corrected splitting approach for convection-diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving probl…
Asymptotic-Preserving Dynamical Low-Rank Method for the Stiff Nonlinear Boltzmann Equation
Lukas Einkemmer, Jingwei Hu, Shiheng Zhang
In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear i…
An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical red…
Automatic partitioning for the low-rank integration of stochastic Boolean reaction networks
Lukas Einkemmer, Julian Mangott, Martina Prugger
Boolean reaction networks are an important tool in biochemistry for studying mechanisms in the biological cell. However, the stochastic formulation of such networks requires the so…
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…
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…