The average utilization, <u>, in a nearest neighbor PDES simulation as a function of NPE—1. One-dimensional simulations with one lattice site per PE (red triangles) and two lattice sites per PE (green diamonds). Two-dimensional Monte Carlo (cyan squares) and n-fold way (black circles) simulations with each PE having a block of lattice sites 128 on a side.

Research Objectives
(1) Test the scalability of parallel discrete event simulations (PDES) on massively parallel computers. (2) Perform large-scale dynamic Monte Carlo simulations related to hysteresis, meta-stbility, and dynamics of domain-wall motion in nanoscale magnetic systems.

Computational Approach
We have implemented Lubachevsky's partially rejection-free method for PDES and used this code to obtain large simulations of hysteresis in Ising models to allow us to obtain nonequilibrium dynamic exponents using finite size scaling techniques. For the study of metastable systems with discrete spins, we utilize the Monte Carlo with absorbing Markov chains algorithm and projective dynamics methods. We include the broad histogram method to enable us to apply these types of algorithms to systems with continuous spins, such as the classical Heisenberg model. We use these methods in stochastic differential equations, in particular Langevin micromagnetic calculations.

Accomplishments
We proved that all conservative implementations of PDES in one dimension (d = 1) are scalable in the calculation phase. We numerically tested our proof of scaling in d = 1, and provided numerical evidence for scaling in d = 2 and d = 3. We used our PDES to perform dynamic Monte Carlo simulations for thermal switching of nanoscale magnets and to perform finite-size scaling for a dynamic phase transition for magnetic thin films. Our dynamic Monte Carlo algorithms allow simulations that are true to the underlying physical dynamic and span very large time scales, from atomistic times to engineering times.

Significance
We proved for the first time that a nontrivial parallelization method is scalable. Since DES are used in a wide variety of fields (from switching of cellular communications networks to war-game simulations), this general proof is of broad interest to researchers in various fields.

Metastability and hysteresis are ubiquitous in materials systems, ranging from ferromagnets to aging and failure of materials. We study both simple models where the physics can be fully explored and understood, and realistic calculations for models of actual systems (nanoscale ferromagnets). The time scales range from microscopic to geologic. To span these disparate time scales, we have introduced novel algorithms that can gain many orders of magnitude in simulation speed, and we have implemented an efficient code for stochastic simulation on a distributed-memory machine, where the pattern of communication between the underlying PEs is completely unpredictable.

Publications
G. Korniss, Z. Toroczkai, M. A. Novotny, and P. A. Rikvold, "From massively parallel algorithms and fluctuating time horizons to non-equilibrium surface growth," Phys. Rev. Lett. 84, 1351 (2000).

G. Korniss, M. A. Novotny, and P. A. Rikvold, "Parallelization of a dynamic Monte Carlo algorithm: A partially rejection-free conservative approach," J. Comp. Phys. 153, 488 (1999).

M. A. Novotny, "A tutorial on advanced dynamic Monte Carlo methods for systems with discrete state spaces," in Annual Reviews of Computational Physics IX, edited by D. Stauffer (World Scientific, Singapore, in press).

http://www.csit.fsu.edu/~novotny