Parallel Computing in the Simulation of Dislocation Dynamics
Introduction
The motion of dislocations, or displacements in the lattice structure
of a crystal, is the primary agent for plastic deformation in metals.
By simulating dislocation motion on a computer, we can easily change
parameters to compare results to those from experiment. The methods
used for such simulations include direct integration of the equations
of motion, finite element analysis, and kinetic Monte Carlo. Kinetic
Monte Carlo, the method of choice for my research, has an added
advantage in that it allows the consideration of stochastic elements,
such as pinning due to impurities, on a more equal footing. Regardless
of the method used, however, the long-range nature of the forces
associated with dislocations as well as the complexity of these forces
leads to a computationally intensive problem involving large data
structures.
Application of parallel computing
As with so many other modeling problems, computing resources are often
the limiting factor in determining the size of the system and the
degree of complexity one can consider in the simulation of dislocation
dynamics. It thus comes as no surprise that scientists in the field have
begun to turn to parallel computing as a way to push this limit.
Several methods have already been developed for approaching the
problem of dislocation motion using parallel algorithms, particularly
for those performing calculations on an atomistic level. A simulation
of crack blunting by dislocation emission involving 3.5 million atoms
was performed by Zhou et. al.. on a CM-5.
(more information)
In the materials science department
at RISØ, in collaboration with the Danish Computing Centre for
Research and Education, a parallel finite element program has been developed
to solve non-linear field equations for the simulation of crystalline
deformation, using a domain-decomposition method implemented by message
passing.
(more information)
Finally, one must not forget the particularly simple method of parallel
Monte Carlo, which simply involves simultaneous independent simulations,
identical except for the random numbers that enter into the evolution of
each trial.
Successes and challenges
The advantages of parallel computing
in such large-scale simulations are precisely those same issues that
are the motivation: with increased speed and size, we may consider
problems that are larger and more complex and thus more accurate.
Considering that dislocation densities in heavily deformed metals can
be as high as several trillion per square centimeter and that a
realistic simulation should be three-dimensional, the size of the data
that must be considered and the number of calculations that must be
performed becomes staggering. While the efforts to overcome these
issues by utilizing parallelization have been largely successful, the
general challenges of data distribution and program portability
remain, as detailed in a by Morris in a discussion of microstructural
calculations (details).
Yet if current proposals for the use of parallel computing resources are any
indication, the applications of parallel computing to dislocation dynamics,
and computational materials science in general, will only increase with time.