We seek to improve the accuracy of uniform grid PIC methods for plasma simulation by applying MR techniques. The development of the new method consists of two separate, but closely related parts: solving the Poisson equation with infinite-domain boundary conditions on non-uniform grids, and charge deposition and field interpolation PIC methods for non-uniform grids.
We have solved the Poisson equation on non-uniform grids with infinite-domain boundary conditions using the James-Lackner boundary potential method. Our implementation uses Chombo, a C++ library to facilitate solution of partial differential equations with finite volume methods on a hierarchy of locally refined grids. Our numerical results shown a second-order convergence rate.
Uniform grid PIC algorithms, when applied to non-uniform
grids, exhibit a well-known error: charged particles
experience a so-called “self-force” due to interaction
with their own fields. This self-force is caused by a
lack of translation-invariance for the discrete Green’s
function in the neighborhood of inter-resolution
interfaces on the non-uniform grids. Our approach is
based on a modified charge deposition algorithm that has
the potential to reduce the self-force error to any
specified degree of accuracy. In the modified method,
particle charges are deposited using a smoothed delta
function convolved with a kernel. The kernel is
calculated by applying the MR Poisson operator to the
exact Green’s function to offset the
translation-invariance error. Analysis and single
particle tests have been conducted to demonstrate the
effectiveness of the new method. Unresolved challenges
regarding its application to continuous charge
distribution problems will be described.
Projector Augmented Wave (PAW) parameter sets can be
constructed in many ways. Due to a non-local expansion of
projectors, the PAW method includes parameters for each
angular momentum channel separately. While this gives the
flexibility to optimize projectors individually, it also
creates an unfathomable parameter space for searching for
good parameter sets. To automatically search for good PAW
sets, logarithmic derivatives were analyzed numerically
for matching with AE logarithmic derivatives. Logarithmic
derivative matching, total energy convergence, and scf
convergence were used as scores for automatic
optimization of ab initio accuracy and speed of PAW
parameter sets using a genetic algorithm within an
optimization code.
The present study introduces a new temporal scaling
method that contributes to resolving the typical
shortcomings of Monte Carlo Potts (MCP) simulations in
the investigation of the conditions and mechanisms that
distinguish recrystallization from dynamic abnormal grain
growth (DAGG). MCP based models are commonly implemented
to simulate microstructural evolution. However, the
numerical implementations of recrystallization and other
deformation-induced phenomena often elude validation due
to the lack of a common temporal scale. The numerical
models for recovery, nucleation and recrystallization
must be analyzed and verified in order to identify the
conditions that initiate or the mechanisms driving DAGG.
The proposed temporal scaling method approaches this
issue by identifying an energetic relationship during
normal grain growth simulations. This energy based
relationship creates the temporal scale for subsequent
simulations of grain boundary migration during
deformation. The applicability of this temporal scaling
approach is investigated by considering a simplistic
static recrystallization model.
Projector Augmented Wave optimization for large scale ab initio calculation
Ryan Snow, A Wright, C. Fong
1. Sand Report Sand 2001-3514, (2002)
2. N.A.W. Holzwrth, A.R. Tackett, and G.E. Matthews,
Computer Physics Communications 135, 329 (2001)
Scaling Issues in the Monte Carlos Potts Simulation of Abnormal Grain Growth in Iron
Corentin Guebels, T. Tran, B. Fell, J. Groza