Graph Coloring Approach to Mesh Generation in Multiphase Media with Smooth Boundaries

Abstract

This paper provides a novel approach for mesh generation for materials that have distinct spatial components with a smooth boundary between them. Experimental data are used in pixel/voxel format to label elements in a generic finite element (FE) mesh of a representative volume element. The basis of this approach is a novel Potts energy formulation to allow integer optimization on the dual of the FE mesh. The Potts energy can be decomposed into two terms: the field energy/data cost and the interaction energy/smoothing cost. The field term is used to represent the likelihood of a grain label on an element based on the experimental voxel data. The interaction term encodes a prior on this labeling; in particular, it is used for smoothening the phase boundary. Energy minimization of this system leads to a multiway cut problem, which is solved using graph cuts. A multilabel energy minimization problem is formulated using a Potts form. This methodology allows capturing smooth boundaries in materials with nonequiaxed morphologies. Applications to polycrystalline microstructures and woven composites are presented. The extension to nonequiaxed morphologies is presented using the Riemannian distance measure. This procedure allows re-usability of an FE mesh by adaptively assigning pixel/voxel information to elements while preserving important features like the phase boundary surface length/area.