Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A low-rank projector-splitting integrator for the Vlasov--Poisson
  equation   Many problems encountered in plasma physics require a description by kinetic
equations, which are posed in an up to six-dimensional phase space. A direct
discretization of this phase space, often called the Eulerian approach, has
many advantages but is extremely expensive from a computational point of view.
In the present paper we propose a dynamical low-rank approximation to the
Vlasov--Poisson equation, with time integration by a particular splitting
method. This approximation is derived by constraining the dynamics to a
manifold of low-rank functions via a tangent space projection and by splitting
this projection into the subprojections from which it is built. This reduces a
time step for the six- (or four-) dimensional Vlasov--Poisson equation to
solving two systems of three- (or two-) dimensional advection equations over
the time step, once in the position variables and once in the velocity
variables, where the size of each system of advection equations is equal to the
chosen rank. By a hierarchical dynamical low-rank approximation, a time step
for the Vlasov--Poisson equation can be further reduced to a set of six (or
four) systems of one-dimensional advection equations, where the size of each
system of advection equations is still equal to the rank. The resulting systems
of advection equations can then be solved by standard techniques such as
semi-Lagrangian or spectral methods. Numerical simulations in two and four
dimensions for linear Landau damping, for a two-stream instability and for a
plasma echo problem highlight the favorable behavior of this numerical method
and show that the proposed algorithm is able to drastically reduce the required
computational effort.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int