Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach

Abstract

We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where the discrete events (updates) are Poisson arrivals. For high performance, we utilize a continuous-time, asynchronous parallel version of the n-fold way rejection-free algorithm. Each processing element carries an lxl block of spins, and we employ the fast SHMEM-library routines on the Cray T3E distributed-memory parallel architecture. Different processing elements have different local simulated times. To ensure causality, the algorithm handles the asynchrony in a conservative fashion. Despite relatively low utilization and an intricate relationship between the average time increment and the size of the spin blocks, we find that for sufficiently large l the algorithm outperforms its corresponding parallel Metropolis (non-rejection-free) counterpart. As an example application, we present results for metastable decay in a model ferromagnetic or ferroelectric film, observed with a probe of area smaller than the total system.

17 pages, 7 figures, RevTex; submitted to the Journal of Computational Physics

References in corpus (7)

• Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition
• Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition
• Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics
• Efficient Parallel Simulations of Asynchronous Cellular Arrays
• A projection method for statics and dynamics of lattice spin systems
• Monte Carlo Simulation of Magnetization Reversal in Fe Sesquilayers on W(110)
• Magnetization Switching in Single-Domain Ferromagnets

Cited by in corpus (22)

• Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field
• Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations
• Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field
• From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth
• Massively parallel Monte Carlo for many-particle simulations on GPUs
• Spatial Dynamics of Invasion: The Geometry of Introduced Species
• Extremal-point Densities of Interface Fluctuations
• Synchronization Landscapes in Small-World-Connected Computer Networks
• Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
• Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition
• On the Evolution of Time Horizons in Parallel and Grid Simulations
• Parallelized Hybrid Monte Carlo Simulation of Stress-Induced Texture Evolution
• Jump Markov Chains and Rejection-Free Metropolis Algorithms
• Algorithmic scalability in globally constrained conservative parallel discrete event simulations of asynchronous systems
• Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers
• Invasive advance of an advantageous mutation: nucleation theory
• Update statistics in conservative parallel discrete event simulations of asynchronous systems
• Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales
• Low-Temperature Long-Time Simulations of Ising Ferromagnets using the Monte Carlo with Absorbing Markov Chains method
• Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamic: effects of the barrier height
• Hybrid Monte Carlo Simulation of Stress-Induced Texture Evolution with Inelastic Effects
• Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems