Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
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
A level set method for thin film epitaxial growth
Journal of Computational Physics
Numerical simulation of grain-boundary grooving by level set method
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
Constructing a computer model of the human eye based on tissue slice images
Journal of Biomedical Imaging
Level Set Based Multispectral Segmentation with Corners
SIAM Journal on Imaging Sciences
Journal of Computational Physics
The Explicit-Implicit-Null method: Removing the numerical instability of PDEs
Journal of Computational Physics
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This paper proposes and implements a novel hybrid level set method which combines the numerical efficiency of the local level set approach with the temporal stability afforded by a semi-implicit technique. By introducing an extraction/insertion algorithm into the local level set approach, we can accurately capture complicated behaviors such as interface separation and coalescence. This technique solves a well known problem when treating a semi-implicit system with spectral methods, where spurious interface movements emerge when two interfaces are close to each other. Numerical experiments show that the proposed method is stable, efficient and scales up well into three dimensional problems.