[HTML][HTML] A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
L Einkemmer, I Joseph - Journal of Computational Physics, 2021 - Elsevier
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-
dimensional phase space. In this context, dynamical low-rank approximations have …
dimensional phase space. In this context, dynamical low-rank approximations have …
A low-rank method for two-dimensional time-dependent radiation transport calculations
Z Peng, RG McClarren, M Frank - Journal of Computational Physics, 2020 - Elsevier
The low-rank approximation is a complexity reduction technique to approximate a tensor or
a matrix with a reduced rank, which has been applied to the simulation of high dimensional …
a matrix with a reduced rank, which has been applied to the simulation of high dimensional …
[HTML][HTML] Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation
L Einkemmer - Journal of Computational Physics, 2024 - Elsevier
We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe
strongly magnetized plasmas. The low-rank approximation is based on a decomposition into …
strongly magnetized plasmas. The low-rank approximation is based on a decomposition into …
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
It has recently been demonstrated that dynamical low-rank algorithms can provide robust
and efficient approximations to a range of kinetic equations. This is true especially if the …
and efficient approximations to a range of kinetic equations. This is true especially if the …
[HTML][HTML] A robust and conservative dynamical low-rank algorithm
L Einkemmer, A Ostermann, C Scalone - Journal of Computational Physics, 2023 - Elsevier
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely
efficient in solving kinetic equations. However, a major deficiency is that it does not preserve …
efficient in solving kinetic equations. However, a major deficiency is that it does not preserve …
A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps
We propose a low-rank tensor approach to approximate linear transport and nonlinear
Vlasov solutions and their associated flow maps. The approach takes advantage of the fact …
Vlasov solutions and their associated flow maps. The approach takes advantage of the fact …
On the stability of robust dynamical low-rank approximations for hyperbolic problems
The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems
that arise in such diverse fields as kinetic transport and uncertainty quantification. Even …
that arise in such diverse fields as kinetic transport and uncertainty quantification. Even …
[HTML][HTML] Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD …
Geophysical flow simulations using hyperbolic shallow water moment equations require an
efficient discretization of a potentially large system of PDEs, the so-called moment system …
efficient discretization of a potentially large system of PDEs, the so-called moment system …
[HTML][HTML] A low-rank complexity reduction algorithm for the high-dimensional kinetic chemical master equation
L Einkemmer, J Mangott, M Prugger - Journal of Computational Physics, 2024 - Elsevier
It is increasingly realized that taking stochastic effects into account is important in order to
study biological cells. However, the corresponding mathematical formulation, the chemical …
study biological cells. However, the corresponding mathematical formulation, the chemical …
A sweep-based low-rank method for the discrete ordinate transport equation
Z Peng, RG McClarren - Journal of Computational Physics, 2023 - Elsevier
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the
solution to matrix differential equations. Recently, the DLR method was applied to radiation …
solution to matrix differential equations. Recently, the DLR method was applied to radiation …