Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauss's Law Satisfying Energy-Conserving Semi-Implicit Particle-in-Cell
  Method   The Energy Conserving Semi-Implicit Method (ECSIM) introduced by Lapenta
(2017) has many advantageous properties compared to the classical semi-implicit
and explicit PIC methods. Most importantly, energy conservation eliminates the
growth of the finite grid instability. We have implemented ECSIM in a different
and more efficient manner than the original approach. More importantly, we have
addressed two major shortcomings of the original ECSIM algorithm: there is no
mechanism to enforce Gauss's law and there is no mechanism to reduce the
numerical oscillations of the electric field. A classical approach to satisfy
Gauss's law is to modify the electric field and its divergence using either an
elliptic or a parabolic/hyperbolic correction based on the Generalized Lagrange
Multiplier method. This correction, however, violates the energy conservation
property, and the oscillations related to the finite grid instability reappear
in the modified ECSIM scheme. We invented a new alternative approach: the
particle positions are modified instead of the electric field in the correction
step. Displacing the particles slightly does not change the energy conservation
property, while it can satisfy Gauss's law by changing the charge density. We
found that the new Gauss's Law satisfying Energy Conserving Semi-Implicit
Method (GL-ECSIM) produces superior results compared to the original ECSIM
algorithm. In some simulations, however, there are still some numerical
oscillations present in the electric field. We attribute this to the simple
finite difference discretization of the energy conserving implicit electric
field solver. We modified the spatial discretization of the field solver to
reduce these oscillations while only slightly violating the energy conservation
properties. We demonstrate the improved quality of the GL-ECSIM method with
several tests.

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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex