Author:

Abstract:

The microstructure of materials often consists of multiple grains with different crystallographic orientations. The study of the evolution of the grains is of great technological importance because many material properties depend on the mean grain size. A common technique to control the grain size of a material is the addition of impurities which leads to the formation of small second-phase particles that will stop the grain growth. The limiting grain size depends on the number, size, shape and spatial distribution of the particles. We employ a phase field model for simulating three-dimensional grain growth in materials containing small incoherent second-phase particles which consists of a large set of coupled reaction-diffusion partial differential equations. A fine threedimensional grid is required to resolve the particles and the shape of the grain boundaries. Moreover, a large number of grains and particles should be considered to achieve statistically relevant results. As such, a typical simulation demands extensive computer resources both with respect to memory and computing time. There are several ways to speed up the computations. We will present two techniques, one using a semi-implicit discretization resulting in an explicit coupling between the partial differential equations so equations can be assigned to different processes and solutions can be computed in parallel. The second technique evolved through a study of the model which revealed that the solutions of the model display small regions of high activity surrounded by large regions of inactivity. This property is exploited through the second technique as we define bounding boxes around the regions of high activity and only solve the equations locally. This algorithm has low memory and computing time requirements.