Simulations of Grain Boundary Evolution via Diffusion-Generated Motion Algorithms
Matthew Elsey, CIMS

Many materials, including most metals and ceramics, are composed of crystallites (often called grains), which are differentiated by their crystallographic orientation. Multiphase weighted motion by mean curvature arises as a classical model describing the annealing of these materials. The distance function-based diffusion-generated  motion (DFDGM) algorithm is introduced and demonstrated to be an accurate and efficient means for simulating this evolution in the case of pure (equally weighted) multiphase motion by curvature. An extension of DFDGM to the more general weighted mean curvature model for grain growth is presented. This extension makes use of a "minimizing motions" idea originally proposed by Almgren, Taylor, and Wang. Results for simple tests have good accuracy properties and are suggestive of numerical convergence. Large-scale simulations are also presented and are shown to agree well with available predictions. Joint work with Selim Esedoglu and Peter Smereka.