A Level Set Approach to Anisotropic Surface Evolution with Free Adatoms

We variationally derive a thermodynamically consistent model for surface evolution under the influence of free adatoms. The resulting system of nonlinear partial differential equations couples a diffusion equation on a surface to the evolution of the surface. A numerical approach based on a finite element discretization of a level set equation is described for an anisotropic evolution, with nonconvex anisotropy functions. Various simulation examples in two and three dimensions demonstrate the applicability of the method. Key words. thin film growth, anisotropic evolution, PDEs on surfaces, higher order evolution equations, level set method, finite elements, adaptivity AMS subject classifications. 35K55, 35R35, 58J32 DOI. 10.1137/060678166

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Christina Stöcker, Axel Voigt
• Keywords: Anisotropic Evolution, Finite Element Discretization, Finite Elements, SIAMAM 2008