Low-rank tensor methods for partial differential equations
M Bachmayr - Acta Numerica, 2023 - cambridge.org
Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …
functions. These concepts, which essentially amount to generalizations of classical …
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 …
An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
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 …
solving the multi-scale multi-dimensional linear transport equation. The method is based on …
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 …
Quantum-inspired method for solving the Vlasov-Poisson equations
E Ye, NFG Loureiro - Physical Review E, 2022 - APS
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 …
are often infeasible due to high-resolution requirements and the exponential scaling of …
A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy
Deterministic models for radiation transport describe the density of radiation particles
moving through a background material. In radiation therapy applications, the phase space of …
moving through a background material. In radiation therapy applications, the phase space of …
[图书][B] Geometric methods on low-rank matrix and tensor manifolds
A Uschmajew, B Vandereycken - 2020 - Springer
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 …
explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus …
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 …
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 …