A level set approach to anisotropic flows with curvature regularization

DOI10.1016/j.jcp.2006.11.026zbMath1201.82049OpenAlexW2107714222MaRDI QIDQ996496

Axel Voigt, Martin Burger, Christina Stöcker, Frank Hausser

Publication date: 14 September 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.11.026

zbMATH Keywords

level set methodshigher-order geometric flowsfacetinganisotropic surface growthcurvature regularization

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Ill-posed problems for PDEs (35R25) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Crystals in solids (74N05) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items

Evolution of elastic thin films with curvature regularization via minimizing movements, Sintering at particle scale: an Eulerian computing framework to deal with strong topological and material discontinuities, The surface diffusion flow with elasticity in the plane, Finite element-based level set methods for higher order flows, The surface diffusion flow with elasticity in three dimensions, High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model, A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis, Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method, Equilibria and dislocations in epitaxial growth, Motion of elastic thin films by anisotropic surface diffusion with curvature regularization, Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization, Surface evolution of elastically stressed films, An energy stable finite difference method for anisotropic surface diffusion on closed curves, 3D finite element simulation of the matter flow by surface diffusion using a level set method

Uses Software

• AMDiS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films
• A finite element method for surface diffusion: the parametric case.
• A discrete scheme for parametric anisotropic surface diffusion
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Motion by intrinsic Laplacian of curvature
• Semi-implicit level set methods for curvature and surface diffusion motion
• A fully discrete numerical scheme for weighted mean curvature flow
• Numerical simulation of anisotropic surface diffusion with curvature-dependent energy
• Evolution of material voids for highly anisotropic surface energy
• A level set formulation for Willmore flow
• A numerical scheme for regularized anisotropic curve shortening flow
• Surface evolution of elastically stressed films under deposition by a diffuse interface model
• An algorithm for the elastic flow of surfaces
• A phase field formulation of the Willmore problem
• OPTIMAL GEOMETRY IN EQUILIBRIUM AND GROWTH
• On Level Set Formulations for Anisotropic Mean Curvature Flow and Surface Diffusion
• Computation of geometric partial differential equations and mean curvature flow
• A Regularized Equation for Anisotropic Motion-by-Curvature
• Some Theorems on the Free Energies of Crystal Surfaces
• An introduction to the adjoint approach to design
• Variational problems and partial differential equations on implicit surfaces