A contribution to the particle modeling of soap films
Applied Mathematics and Computation
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
The discrete plateau problem: algorithm and numerics
Mathematics of Computation
Fast tree-based redistancing for level set computations
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Local level set method in high dimension and codimension
Journal of Computational Physics
Differential geometry based solvation model I: Eulerian formulation
Journal of Computational Physics
| Hi-index | 31.46 |
In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries. The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary in R^n under mean curvature flow. For n=3 the problem has been approached in D.L. Chopp, 1993 and L.-T. Cheng [D.L. Chopp, Computing minimal surfaces via level set curvature flow, J. Comput. Phys. 106(1) (1993) 77-91 and L.-T. Cheng, The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using the level set method, but with a more complicated boundary conditions. The method we present can be generalized straightforward to arbitrary dimension, and the framework in which it is presented is dimension independent. Examples are shown for n=2, 3, 4.