Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics (Communications in Computational Physics, 2009)
Geometrical evolution laws are widely used in continuum modeling of surfaceand interface motion in materials science. In this article, we first give a brief reviewof various kinds of geometrical evolution laws and their variational derivations,with an emphasis on strong anisotropy. We then survey some of the finite elementbased numerical methods for simulating the motion of interfaces focusing on the fieldof thin film growth. We discuss the finite element method applied to front-tracking,phase-field and level-set methods. We describe various applications of these geometricalevolution laws to materials science problems, and in particular, the growth andmorphologies of thin crystalline films.