Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Motion of multiple junctions: a level set approach
Journal of Computational Physics
A simple proof of convergence for an approximation scheme for computing motions by mean curvature
SIAM Journal on Numerical Analysis
A numerical method for tracking curve networks moving with curvature motion
Journal of Computational Physics
A dynamic mesh algorithm for curvature dependent evolving interfaces
Journal of Computational Physics
Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg-Landau equation
SIAM Journal on Mathematical Analysis
Capturing the behavior of bubbles and drops using the variational level set approach
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
Convolution-generated motion as a link between cellular automata and continuum pattern dynamics
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Convolution-generated motion and generalized Huygens' principles for interface motion
SIAM Journal on Applied Mathematics
Convolution—thresholding methods for interface motion
Journal of Computational Physics
Efficient algorithms for diffusion-generated motion by mean curvature
Efficient algorithms for diffusion-generated motion by mean curvature
Diffusion generated motion of curves on surfaces
Journal of Computational Physics
A Novel Method for Enhanced Needle Localization Using Ultrasound-Guidance
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
SIAM Journal on Scientific Computing
Algorithms for Area Preserving Flows
SIAM Journal on Scientific Computing
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
A variational method for multiphase volume-preserving interface motions
Journal of Computational and Applied Mathematics
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In this article, we present a diffusion-generated approach for evolving volume-preserving motion by mean curvature. Our algorithm alternately diffuses and sharpens characteristic functions to produce a normal velocity which equals the mean curvature minus the average mean curvature. This simple algorithm naturally treats topological mergings and breakings and can be made very fast even when the volume constraint is enforced to double precision (or more). Two dimensional numerical studies are provided to demonstrate the convergence of the method for smooth and nonsmooth problems.