Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Crystal growth and dendritic solidification
Journal of Computational Physics
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
Evolutionary fronts for topology-independent shape modeling and recovery
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
A fast level set method for propagating interfaces
Journal of Computational Physics
An Eulerian approach for vortex motion using a level set regularization procedure
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
SIAM Review
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Maintaining the point correspondence in the level set framework
Journal of Computational Physics
Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
SIAM Journal on Scientific Computing
A Second-Order Accurate Conservative Front-Tracking Method in One Dimension
SIAM Journal on Scientific Computing
Simulating Biochemical Signaling Networks in Complex Moving Geometries
SIAM Journal on Scientific Computing
Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids
Journal of Computational Physics
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
Closest point turbulence for liquid surfaces
ACM Transactions on Graphics (TOG)
An embedded boundary method for soluble surfactants with interface tracking for two-phase flows
Journal of Computational Physics
Hi-index | 31.50 |
We develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework. Level set methods are computational techniques for tracking moving interfaces; they work by embedding the propagating interface as the zero level set of a higher dimensional function, and then approximate the solution of the resulting initial value partial differential equation using upwind finite difference schemes. The traditional level set method works in the trace space of the evolving interface, and hence disregards any parameterization in the interface description. Consequently, material quantities on the interface which themselves are transported under the interface motion are not easily handled in this framework. We develop model equations and algorithmic techniques to extend the level set method to include these problems. We demonstrate the accuracy of our approach through a series of test examples and convergence studies.