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
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
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
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Physica D
A remark on computing distance functions
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
A convergent monotone difference scheme for motion of level sets by mean curvature
Numerische Mathematik
SIAM Journal on Numerical Analysis
A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Contour Detection for Industrial Image Processing by Means of Level Set Methods
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Automatica (Journal of IFAC)
Optimization of Convex Shapes: An Approach to Crystal Shape Identification
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem
Automatica (Journal of IFAC)
Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation
Computers in Biology and Medicine
A stochastic reach-avoid problem with random obstacles
Proceedings of the 14th international conference on Hybrid systems: computation and control
Modeling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback
SIAM Journal on Scientific Computing
Physically based simulation of solid objects' burning
Transactions on Edutainment VII
Modeling actin cable contraction
Computers & Mathematics with Applications
One-shot computation of reachable sets for differential games
Proceedings of the 16th international conference on Hybrid systems: computation and control
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Level set methods are a popular and powerful class of numerical algorithms for dynamic implicit surfaces and solution of Hamilton-Jacobi PDEs. While the advanced level set schemes combine both efficiency and accuracy, their implementation complexity makes it difficult for the community to reproduce new results and make quantitative comparisons between methods. This paper describes the Toolbox of Level Set Methods, a collection of Matlab routines implementing the basic level set algorithms on fixed Cartesian grids for rectangular domains in arbitrary dimension. The Toolbox's code and interface are designed to permit flexible combinations of different schemes and PDE forms, allow easy extension through the addition of new algorithms, and achieve efficient execution despite the fact that the code is entirely written as m-files. The current contents of the Toolbox and some coding patterns important to achieving its flexibility, extensibility and efficiency are briefly explained, as is the process of adding two new algorithms. Code for both the Toolbox and the new algorithms is available from the Web.