This document describes a toolbox of level set methods for solving time-dependent Hamilton-Jacobi partial differential equations (PDEs) in the Matlab programming environment. Level set methods are often used for simulation of dynamic implicit surfaces in graphics, fluid and combustion simulation, image processing, and computer vision. Hamilton-Jacobi and related PDEs arise in fields such as control, robotics, differential games, dynamic programming, mesh generation, stochastic differential equations, financial mathematics, and verification. The algorithms in the toolbox can be used in any number of dimensions, although computational cost and visualization difficulty make dimensions four and higher a challenge. All source code for the toolbox is provided as plain text in the Matlab m-file programming language. The toolbox is designed to allow quick and easy experimentation with level set methods, although it is not by itself a level set tutorial and so should be used in combination with the existing literature.

References in zbMATH (referenced in 39 articles , 1 standard article )

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  1. Botkin, Nikolai; Turova, Varvara; Diepolder, Johannes; Bittner, Matthias; Holzapfel, Florian: Aircraft control during cruise flight in windshear conditions: viability approach (2017)
  2. Xu, Li; Wang, Jin: Quantifying the potential and flux landscapes of multi-locus evolution (2017)
  3. Zanon, Mario; Boccia, Andrea; Palma, Vryan Gil S.; Parenti, Sonja; Xausa, Ilaria: Direct optimal control and model predictive control (2017)
  4. Mohajerin Esfahani, Peyman; Chatterjee, Debasish; Lygeros, John: The stochastic reach-avoid problem and set characterization for diffusions (2016)
  5. Ghanbarzadeh, Soheil; Hesse, Marc A.; Prodanović, Maša: A level set method for materials with texturally equilibrated pores (2015)
  6. Govindarajan, Nithin; de Visser, Cornelis. C.; Krishnakumar, Kalmanje: A sparse collocation method for solving time-dependent HJB equations using multivariate $B$-splines (2014)
  7. Kurzhanski, Alexander B.; Varaiya, Pravin: Dynamics and control of trajectory tubes. Theory and computation (2014)
  8. Lesser, Kendra; Oishi, Meeko: Reachability for partially observable discrete time stochastic hybrid systems (2014)
  9. Takei, Ryo; Tsai, Richard; Zhou, Zhengyuan: An efficient algorithm for a visibility-based surveillance-evasion game (2014)
  10. Mitchell, Ian M.; Kaynama, Shahab; Chen, Mo; Oishi, Meeko: Safety preserving control synthesis for sampled data systems (2013)
  11. Nabi, Ali; Mirzadeh, Mohammad; Gibou, Frederic; Moehlis, Jeff: Minimum energy desynchronizing control for coupled neurons (2013)
  12. Summers, Erin; Chakraborty, Abhijit; Tan, Weehong; Topcu, Ufuk; Seiler, Peter; Balas, Gary; Packard, Andrew: Quantitative local $L_2$-gain and reachbility analysis for nonlinear systems (2013)
  13. Almeida, Luís; Bagnerini, Patrizia; Habbal, Abderrahmane: Modeling actin cable contraction (2012)
  14. Zhuang, X.; Augarde, C. E.; Mathisen, K. M.: Fracture modeling using meshless methods and level sets in 3D: framework and modeling (2012)
  15. Grepl, Martin A.; Veroy, Karen: A level set reduced basis approach to parameter estimation (2011)
  16. Papadopoulos, Dimitris; Herty, Michael; Rath, Volker; Behr, Marek: Identification of uncertainties in the shape of geophysical objects with level sets and the adjoint method (2011)
  17. Tyatyushkin, A. I.; Morzhin, O. V.: Numerical investigation of attainability sets of nonlinear controlled differential systems (2011)
  18. Balzer, Jonathan: Second-order domain derivative of normal-dependent boundary integrals (2010)
  19. Bect, Julien: A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems (2010)
  20. Summers, Sean; Lygeros, John: Verification of discrete time stochastic hybrid systems: a stochastic reach-avoid decision problem (2010)

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