Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A regularized equation for anisotropic motion-by-curvature
SIAM Journal on Applied Mathematics
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
A finite element method for surface diffusion: the parametric case
Journal of Computational Physics
Numerical simulation of anisotropic surface diffusion with curvature-dependent energy
Journal of Computational Physics
Surface evolution of elastically stressed films under deposition by a diffuse interface model
Journal of Computational Physics
AMDiS: adaptive multidimensional simulations
Computing and Visualization in Science
Finite Element-Based Level Set Methods for Higher Order Flows
Journal of Scientific Computing
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Modeling and simulation of faceting effects on surfaces are topics of growing importance in modern nanotechnology. Such effects pose various theoretical and computational challenges, since they are caused by non-convex surface energies, which lead to ill-posed evolution equations for the surfaces. In order to overcome the ill-posedness, regularization of the energy by a curvature-dependent term has become a standard approach, which seems to be related to the actual physics, too. The use of curvature-dependent energies yields higher order partial differential equations for surface variables, whose numerical solution is a very challenging task. In this paper, we investigate the numerical simulation of anisotropic growth with curvature-dependent energy by level set methods, which yield flexible and robust surface representations. We consider the two dominating growth modes, namely attachment-detachment kinetics and surface diffusion. The level set formulations are given in terms of metric gradient flows, which are discretized by finite element methods in space and in a semi-implicit way as local variational problems in time. Finally, the constructed level set methods are applied to the simulation of faceting of embedded surfaces and thin films.