Polycrystalline materials, a class which includes most metals and ceramics, are composed of a large aggregate of single crystal pieces called grains. The Kobayashi-Warren-Carter (KWC) model is a fundamental model in material science for simulating grain microstructure evolution. The KWC energy depends on two variables,  which records the orientation of the grains, and  which acts as an indicator function for the grain boundaries. Accurately computing KWC gradient flows is difficult to due to the interactions of the  and  equations along with the presence of non-smooth terms in the KWC functional.
In this work, we propose a new computational approach for the time evolution of the KWC model. We solve the  evolution equation independently of the problem size using the techniques recently developed G-prox PDHG algorithm of Jacobs et al. We also develop a novel thresholding technique, which allows us to compute the theta evolution almost instantaneously without requiring an iterative method. Our method is substantially faster than standard methods for evolving the KWC equations, and has the added benefit of producing sharp grain boundaries at every time step. We anticipate that our new approach will allow for much larger scale simulations than were previously possible.

Author: Matthew Jacobs