Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-Helmholtz Decomposition, Gauss' Laws and Charge Conservation for
  Finite Element Particle-in-Cell   Development of particle in cell methods using finite element based methods
(FEMs) have been a topic of renewed interest; this has largely been driven by
(a) the ability of finite element methods to better model geometry, (b) better
understanding of function spaces that are necessary to represent all Maxwell
quantities, and (c) more recently, the fundamental rubrics that should be
obeyed in space and time so as to satisfy Gauss' laws and the equation of
continuity. In that vein, methods have been developed recently that satisfy
these equations and are agnostic to time stepping methods. While is development
is indeed a significant advance, it should be noted that implicit FEM transient
solvers support an underlying null space that corresponds to a gradient of a
scalar potential $\nabla \Phi(\textbf{r})$ (or $t \nabla \Phi (\textbf{r})$ in
the case of wave equation solvers). While explicit schemes do not suffer from
this drawback, they are only conditionally stable, time step sizes are mesh
dependent, and very small. A way to overcome this bottleneck, and indeed,
satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on
a tessellation. In the re-formulation presented, we strictly satisfy the
equation of continuity and Gauss' laws for both the electric and magnetic flux
densities. Results demonstrating the efficacy of this scheme will be presented.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph