In recent years, there has been significant interest in continuum models of crystal surface evolution and facet formation. However, in the most physically relevant case, when the free energy of the surface is the total variation energy, even existence of solutions to the continuum PDE is unknown. Furthermore, attempts at developing a robust numerical method for simulating solutions suffer from significant stiffness, preventing numerical study of the equation’s behavior on fine spatial grids. In this talk, I will describe a new approach to simulating solutions of the crystal surface evolution equation based on combining the formal gradient flow structure of this equation with modern operator splitting techniques. This is based on joint work with Jian-Guo Liu, Jianfeng Lu, Jeremy L. Marzuola, and Li Wang.

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