Improvement of an advanced kinetic Monte Carlo algorithm through storing and recycling factorised transition matrices

Sammanfattning: The Kinetic Monte Carlo algorithm is a universal method to simulate the evolution of systems governed by a master equation. However, this approach is severely limited by the kinetic trapping of the simulated trajectories in low energy basins. To alleviate this issue, non-local transitions escaping the trapping basins are performed based on a factorisation of the transition matrix associated with the master equation. Whenever trapping becomes severe, the simulation repeatedly visits a limited number of basins and performs the same factorisations many times. In this report, we present two methods aiming at further improving the efficiency of the factorised Kinetic Monte Carlo algorithm. The first method consists of storing and recycling the transition matrix factorisations, while the second method constructs on-the-fly a graph connecting the factorised transition matrices. The efficiency of these methods is demonstrated on simulations of cluster migration in an iron-based alloy.