A vertex model of recrystallization with stored energy implemented in GPU

Abstract

Recrystallization models and simulations have been the subject of much attention in materials community in the past decades due to this process having a significant effect on many technologically important materials characteristics. Statistical analysis performed close to the steady state requires large-scale simulations, which are often prohibitively expensive from computational point of view. Graphical Processing Unit (GPU)-based realizations provide a viable approach to addressing this challenge, yet they remain relatively under-explored in this context.In the present manuscript, we develop a fully-parallelizable matrix-free GPU-based algorithm for implementing a two-dimensional vertex model of recrystallization based on the stored energy formalism. Nucleation is assumed to take place at triple junctions and obeys a Metropolis-type criterion. We include a complete mathematical analysis of the nucleation model deriving conditions under which nucleation is successful. Stability analysis of the dynamics of a triple junction under the presence of bulk energy is provided. On the computational side, we propose a novel polling system for handling topological transitions to ensure robust GPU implementation. Single grain tests are performed for benchmarking purposes. Finally, a set of numerical experiments for large scale systems is presented to explore the effect of initial distributions of stored energy on several statistical characteristics.