Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A positivity-preserving high-order semi-Lagrangian discontinuous
  Galerkin scheme for the Vlasov-Poisson equations   The Vlasov-Poisson equations describe the evolution of a collisionless
plasma, represented through a probability density function (PDF) that
self-interacts via an electrostatic force. One of the main difficulties in
numerically solving this system is the severe time-step restriction that arises
from parts of the PDF associated with moderate-to-large velocities. The
dominant approach in the plasma physics community for removing these time-step
restrictions is the so-called particle-in-cell (PIC) method, which discretizes
the distribution function into a set of macro-particles, while the electric
field is represented on a mesh. Several alternatives to this approach exist,
including fully Lagrangian, fully Eulerian, and so-called semi-Lagrangian
methods. The focus of this work is the semi-Lagrangian approach, which begins
with a grid-based Eulerian representation of both the PDF and the electric
field, then evolves the PDF via Lagrangian dynamics, and finally projects this
evolved field back onto the original Eulerian mesh. In particular, we develop
in this work a method that discretizes the 1+1 Vlasov-Poisson system via a
high-order discontinuous Galerkin (DG) method in phase space, and an operator
split, semi-Lagrangian method in time. Second-order accuracy in time is
relatively easy to achieve via Strang operator splitting. With additional work,
using higher-order splitting and a higher-order method of characteristics, we
also demonstrate how to push this scheme to fourth-order accuracy in time. We
show how to resolve all of the Lagrangian dynamics in such a way that mass is
exactly conserved, positivity is maintained, and high-order accuracy is
achieved. The Poisson equation is solved to high-order via the smallest stencil
local discontinuous Galerkin (LDG) approach. We test the proposed scheme on
several standard test cases.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex