Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 though it is well known that certain spatial and temporal
discretizations when combined with the DLRA approach can result in numerical
instability, this phenomenon is poorly understood. In this paper we perform a
$L^2$ stability analysis for the corresponding nonlinear equations of motion.
This reveals the source of the instability for the projector splitting
integrator when first discretizing the equations and then applying the DLRA.
Based on this we propose a projector splitting integrator, based on applying
DLRA to the continuous system before performing the discretization, that
recovers the classic CFL condition. We also show that the unconventional
integrator has more favorable stability properties and explain why the
projector splitting integrator performs better when approximating higher
moments, while the unconventional integrator is generally superior for first
order moments. Furthermore, an efficient and stable dynamical low-rank update
for the scattering term in kinetic transport is proposed. Numerical experiments
for kinetic transport and uncertainty quantification, which confirm the results
of the stability analysis, are presented.

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess