Evolution of two-dimensional grain boundary networks implemented in GPU.

Graphical abstract Highlights • Continuous transition between vertex-driven and curvature-driven models. • Extensive set of statistics computed. • Several choices of grain boundary energy considered, including the Read-Shockley energy. Abstract We consider a variational model for two-dimensional grain growth that allows for finite mobilities of boundaries and boundary junctions. We use a collocation method to describe the grain boundaries and posit evolution equations that ensure energy dissipation. The resulting algorithm is amenable to parallelization and a GPU implementation described in this work leads to significant reduction in computational time. We benchmark our code against known numerical and analytical solutions in some special cases. We also conduct an extensive analysis of statistics that develop for various parameter regimes. [ABSTRACT FROM AUTHOR]