Progress in the Development of a 3D Finite Element PIC code
T. Bui, Calabazas Creek Research

Abstract: We will present the self heating results from loading
particles in unstructured meshes. The problem domain can be either
orthogonal or nonorthogonal. Particle positions are loaded either
spatially uniform or by an inversion of the cumulative density. The
inversion of the cumulative distribution functions requires a
combination of distribution numbers and functions. The distribution of
numbers can be either uniform, random or quiet. The distribution
function can be either uniform, Gaussian or arbitrary. We will also
present the results of 1D uniform cold plasma oscillation due to an
initial sinusoidal perturbation in a 3D finite element simulation.
Due to the unexpected exponential growth in particle kinetic energies
in both self-heating and 1D simple harmonic motion analysis, the
underlying finite element formulation will be provided so that the
causes for this exponential energy growth can be explained. The
Superconvergent Patch Recovery (SPR) method, which is used to
post-process the finite element solution to obtain a C0-continuous
electric field, will also be described to illustrate probable causes
due to the discontinuity of the electric field across the finite
element boundaries and the coupling of other two other electric field
components to the active component in 1D problem solved by a 3D code.
In addition, the major advantage to have a C0-continuous electric
field produced by the SPR method is to have the same interpolation
order for both electric and charge density fields in solving the
Lorentz equations of motion.