Motion of multiple junctions: a level set approach
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
Efficient algorithms for diffusion-generated motion by mean curvature
Journal of Computational Physics
A diffusion-generated approach to multiphase motion
Journal of Computational Physics
A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions
SIAM Journal on Applied Mathematics
A remark on computing distance functions
Journal of Computational Physics
Convolution—thresholding methods for interface motion
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
A Variational Approach to Modeling and Simulation of Grain Growth
SIAM Journal on Scientific Computing
Diffusion generated motion using signed distance functions
Journal of Computational Physics
Analysis and applications of the Voronoi Implicit Interface Method
Journal of Computational Physics
Hi-index | 31.46 |
An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware.