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 …

We propose a dynamical low-rank method to reduce the computational complexity for
solving the multi-scale multi-dimensional linear transport equation. The method is based on …

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 …

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation
are often infeasible due to high-resolution requirements and the exponential scaling of …

Deterministic models for radiation transport describe the density of radiation particles
moving through a background material. In radiation therapy applications, the phase space of …

In this chapter we present numerical methods for low-rank matrix and tensor problems that
explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus …

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 …