Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
Subdivisions and triangulations of polytopes
Handbook of discrete and computational geometry
Tree methods for moving interfaces
Journal of Computational Physics
Fast tree-based redistancing for level set computations
Journal of Computational Physics
The ghost fluid method for deflagration and detonation discontinuities
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Computer Vision and Image Understanding
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Simplicial isosurfacing in arbitrary dimension and codimension
Journal of Computational Physics
IEEE Transactions on Image Processing
A numerical method for computing minimal surfaces in arbitrary dimension
Journal of Computational Physics
On the Evolution of Vector Distance Functions of Closed Curves
International Journal of Computer Vision
Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Out-of-core and compressed level set methods
ACM Transactions on Graphics (TOG)
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
Efficient level set methods for constructing wavefronts in three spatial dimensions
Journal of Computational Physics
Essentially Non-Oscillatory Adaptive Tree Methods
Journal of Scientific Computing
Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics
Journal of Scientific Computing
Journal of Computational Physics
A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations
Journal of Computational Physics
Journal of Computational Physics
A Memory and Computation Efficient Sparse Level-Set Method
Journal of Scientific Computing
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
Out-of-Core Computations of High-Resolution Level Sets by Means of Code Transformation
Journal of Scientific Computing
Regularization of mappings between implicit manifolds of arbitrary dimension and codimension
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Journal of Scientific Computing
A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids
Journal of Scientific Computing
VDB: High-resolution sparse volumes with dynamic topology
ACM Transactions on Graphics (TOG)
Hi-index | 31.50 |
A new method is presented for numerically capturing a moving interface of arbitrary dimension and codimension. The method is named the 'local level set method', since it localizes the level set method near the interface to significantly reduce the computational expense of the level set method. Following the framework of the level set method, an interface is implicitly represented as the zero level set of a vector valued function. A spatial tree structure is used to locally sample the vector valued function near the interface. Using a Lipschitz stable interpolation and a semi-Lagrangian scheme, our method is stable under both the maximum norm and the Lipschitz semi-norm. Due to this stability, the method does not need to reinitialize a level set function. Several numerical examples with high codimension are successfully tested.