515 research outputs found
Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems
An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm
developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008)
3804] to discrete lattices is presented. The method solves the master equation
synchronously by recourse to null events that keep all processors time clocks
current in a global sense. Boundary conflicts are rigorously solved by adopting
a chessboard decomposition into non-interacting sublattices. We find that the
bias introduced by the spatial correlations attendant to the sublattice
decomposition is within the standard deviation of the serial method, which
confirms the statistical validity of the method. We have assessed the parallel
efficiency of the method and find that our algorithm scales consistently with
problem size and sublattice partition. We apply the method to the calculation
of scale-dependent critical exponents in billion-atom 3D Ising systems, with
very good agreement with state-of-the-art multispin simulations
Phase transition between synchronous and asynchronous updating algorithms
We update a one-dimensional chain of Ising spins of length with
algorithms which are parameterized by the probability for a certain site to
get updated in one time step. The result of the update event itself is
determined by the energy change due to the local change in the configuration.
In this way we interpolate between the Metropolis algorithm at zero temperature
for of the order of 1/L and for large , and a synchronous deterministic
updating procedure for . As function of we observe a phase transition
between the stationary states to which the algorithm drives the system. These
are non-absorbing stationary states with antiferromagnetic domains for ,
and absorbing states with ferromagnetic domains for . This means
that above this transition the stationary states have lost any remnants to the
ferromagnetic Ising interaction. A measurement of the critical exponents shows
that this transition belongs to the universality class of parity conservation.Comment: 5 pages, 3 figure
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU
Monte Carlo simulations of the Ising model play an important role in the
field of computational statistical physics, and they have revealed many
properties of the model over the past few decades. However, the effect of
frustration due to random disorder, in particular the possible spin glass
phase, remains a crucial but poorly understood problem. One of the obstacles in
the Monte Carlo simulation of random frustrated systems is their long
relaxation time making an efficient parallel implementation on state-of-the-art
computation platforms highly desirable. The Graphics Processing Unit (GPU) is
such a platform that provides an opportunity to significantly enhance the
computational performance and thus gain new insight into this problem. In this
paper, we present optimization and tuning approaches for the CUDA
implementation of the spin glass simulation on GPUs. We discuss the integration
of various design alternatives, such as GPU kernel construction with minimal
communication, memory tiling, and look-up tables. We present a binary data
format, Compact Asynchronous Multispin Coding (CAMSC), which provides an
additional speedup compared with the traditionally used Asynchronous
Multispin Coding (AMSC). Our overall design sustains a performance of 33.5
picoseconds per spin flip attempt for simulating the three-dimensional
Edwards-Anderson model with parallel tempering, which significantly improves
the performance over existing GPU implementations.Comment: 15 pages, 18 figure
A rigorous sequential update strategy for parallel kinetic Monte Carlo simulation
The kinetic Monte Carlo (kMC) method is used in many scientific fields in
applications involving rare-event transitions. Due to its discrete stochastic
nature, efforts to parallelize kMC approaches often produce unbalanced time
evolutions requiring complex implementations to ensure correct statistics. In
the context of parallel kMC, the sequential update technique has shown promise
by generating high quality distributions with high relative efficiencies for
short-range systems. In this work, we provide an extension of the sequential
update method in a parallel context that rigorously obeys detailed balance,
which guarantees exact equilibrium statistics for all parallelization settings.
Our approach also preserves nonequilibrium dynamics with minimal error for many
parallelization settings, and can be used to achieve highly precise sampling
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