Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy-stable positivity-preserving DG schemes for Boltzmann-Poisson
  models of collisional electronic transport along energy bands   This work develops entropy-stable positivity-preserving DG methods as a
computational scheme for Boltzmann-Poisson systems modeling the pdf of
electronic transport along energy bands in semiconductor crystal lattices. We
pose, using spherical or energy-angular variables as momentum coordinates, the
corresponding Vlasov Boltzmann eq. with a linear collision operator with a
singular measure modeling the scattering as functions of the energy band. We
show stability results of semi-discrete DG schemes under an entropy norm for
1D-position 2D-momentum, and 2D-position 3D-momentum, using the dissipative
properties of the collisional operator given its entropy inequality, which
depends on the whole Hamiltonian rather than only the kinetic energy. For the
1D problem, knowledge of the analytic solution to Poisson and of the
convergence to a constant current is crucial to obtain full stability. For the
2D problem, specular reflection BC are considered in addition to periodicity in
the estimate for stability under an entropy norm. Regarding positivity
preservation (1D position), we treat the collision operator as a source term
and find convex combinations of the transport and collision terms which
guarantee the positivity of the cell average of our numerical pdf at the next
time step. The positivity of the numerical pdf in the whole domain is
guaranteed by applying the natural limiters that preserve the cell average but
modify the slope of the piecewise linear solutions in order to make the
function non-negative. The use of a spherical coordinate system
$\vec{p}(|\vec{p}|,\mu=cos\theta,\varphi)$ is slightly different to the choice
in previous DG solvers for BP, since the proposed DG formulation gives simpler
integrals involving just piecewise polynomial functions for both transport and
collision terms, which is more adequate for Gaussian quadrature than previous
approaches.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc