2 research outputs found
Fast electrostatic solvers for kinetic Monte Carlo simulations
Kinetic Monte Carlo (KMC) is an important computational tool in physics and
chemistry. In contrast to standard Monte Carlo, KMC permits the description of
time dependent dynamical processes and is not restricted to systems in
equilibrium. Recently KMC has been applied successfully in modelling of novel
energy materials such as Lithium-ion batteries and solar cells. We consider
general solid state systems which contain free, interacting particles which can
hop between localised sites in the material. The KMC transition rates for those
hops depend on the change in total potential energy of the system. For charged
particles this requires the frequent calculation of electrostatic interactions,
which is usually the bottleneck of the simulation. To avoid this issue and
obtain results in reasonable times, many studies replace the long-range
potential by a short range approximation. This, however, leads to systematic
errors and unphysical results. On the other hand standard electrostatic solvers
such as Ewald summation or fast Poisson solvers are highly inefficient or
introduce uncontrollable systematic errors at high resolution. In this paper we
describe how the Fast Multipole Method by Greengard and Rokhlin can be adapted
to overcome this issue by dramatically reducing computational costs. We exploit
the fact that each update in the transition rate calculation corresponds to a
single particle move and changes the configuration only by a small amount. This
allows us to construct an algorithm which scales linearly in the number of
charges for each KMC step, something which had not been deemed to be possible
before. We demonstrate the performance and parallel scalability of the method
by implementing it in a performance portable software library. We describe the
high-level Python interface of the code which makes it easy to adapt to
specific cases.Comment: 26 pages, 19 figures, 7 tables; accepted for publication in Computer
Physics Communication