Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Level sets of viscosity solutions: some applications to fronts and rendez-vous problems
SIAM Journal on Applied Mathematics
Computation of three dimensional dendrites with finite elements
Journal of Computational Physics
Evolution of Convex Plane Curves Describing Anistropic Motions of Phase Interfaces
SIAM Journal on Scientific Computing
Algorithms for Computing Motion by Mean Curvature
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Computational and qualitative aspects of evolution of curves driven by curvature and external force
Computing and Visualization in Science
A convergent monotone difference scheme for motion of level sets by mean curvature
Numerische Mathematik
A conservative level set method for two phase flow
Journal of Computational Physics
Mass preserving finite element implementations of the level set method
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
SIAM Journal on Scientific Computing
Segmentation of 3D cell membrane images by PDE methods and its applications
Computers in Biology and Medicine
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We introduce a new computational technique for evolving interfaces, the flux-based level set method. A nonlinear degenerate advection-diffusion level set equation is discretized by a finite volume method using a complementary volume strategy. It enables to solve the problem in an efficient and stable way. Using a flux-based method of characteristics for the advective part and a semi-implicit treatment of diffusive part, it removes the standard CFL condition on time step and it decreases CPU times significantly. The method is presented for 2D and 3D interface motions driven in normal direction by a constant and spatially varying driving force and (mean) curvature. Comparisons with known exact solutions and further numerical experiments, including topological changes of the interface, are presented.