[Paper Review] Parallelization of a Dynamic Monte Carlo Algorithm

G. Korniss, M. A. Novotny+1 more|arXiv (Cornell University)|Aug 10, 1999

Theoretical and Computational Physics36 references43 citations

TL;DR

This paper presents a scalable, continuous-time, asynchronous parallel implementation of the n-fold way algorithm for dynamic Monte Carlo simulations in kinetic Ising models. By using block-wise spin updates with one-sided communication and conservative causality enforcement, it achieves better performance than non-rejection-free parallel Metropolis methods for large system sizes, particularly in simulating metastable decay in ferromagnetic or ferroelectric films.

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 l×l block of spins, and we employ fast one-sided communication routines on a 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 the algorithm is scalable and for sufficiently large l it outperforms its corresponding parallel Metropolis (non-rejection-free) counterpart. As a sample 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.

Motivation & Objective

• To develop a highly scalable, parallel algorithm for simulating metastable decay in kinetic Ising models.
• To overcome limitations of traditional parallel Metropolis algorithms by using a rejection-free, continuous-time approach.
• To enable efficient simulation of rare events in stochastic cellular automata with Poisson-distributed updates.
• To ensure causality in a distributed-memory environment with asynchronous processing elements having different local times.

Proposed method

• The algorithm uses a continuous-time, asynchronous n-fold way approach to avoid rejection steps in event selection.
• Each processing element manages an l×l block of spins, maintaining its own local simulated time.
• One-sided communication routines are employed to minimize synchronization overhead in distributed-memory architectures.
• Causality is preserved through conservative handling of asynchronous updates, ensuring physically consistent simulation order.
• The method is generalized to other stochastic cellular automata with Poisson-distributed discrete events.
• The algorithm's performance is evaluated by comparing it to a parallel Metropolis implementation under identical conditions.

Experimental results

Research questions

• RQ1 Can a rejection-free, continuous-time parallel algorithm scale effectively on distributed-memory systems for kinetic Ising models?
• RQ2 How does the performance of the asynchronous n-fold way compare to the parallel Metropolis algorithm in simulating metastable decay?
• RQ3 What impact does block size (l×l) have on the average time increment and overall efficiency of the parallel algorithm?
• RQ4 How does asynchrony in local simulated times affect the accuracy and scalability of the simulation?
• RQ5 Can the algorithm efficiently capture rare events like metastable decay in ferroelectric or ferromagnetic films?

Key findings

• The proposed algorithm is scalable and outperforms the corresponding parallel Metropolis algorithm for sufficiently large block sizes (l).
• Despite relatively low utilization and complex scaling between time increment and block size, the algorithm maintains good performance on large systems.
• The asynchronous, conservative update strategy successfully preserves causality across distributed processing elements with differing local times.
• The method enables accurate observation of metastable decay in a probe area smaller than the total system size.
• The rejection-free nature of the n-fold way reduces computational overhead compared to Metropolis-based approaches, especially in systems with rare events.
• The algorithm demonstrates practical applicability to real materials simulations, such as ferromagnetic or ferroelectric thin films.