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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …