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Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains (1997)  (Make Corrections)  (22 citations)
Timothy J. Barth, James A. Sethian



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Abstract: Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a "virtual" edge ipping technique, Lipschitz continuity of the numerical flux is restored on... (Update)

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BibTeX entry:   (Update)

Barth T., and Sethian, J.A., Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains, submitted for publication, J. Comp. Phys., 1997. http://citeseer.ist.psu.edu/barth97numerical.html   More

@misc{ barth97numerical,
  author = "T. Barth and J. Sethian",
  title = "Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated
    Domains",
  note = "submitted for publication, J. Comp. Phys., 1997.",
  year = "1997",
  url = "citeseer.ist.psu.edu/barth97numerical.html" }
Citations (may not include all citations):
567   Fronts propagating with curvature dependent speed: Algorithm.. - Osher, Sethian - 1988
136   A fast level set method for propagating interfaces - Adalsteinsson, Sethian - 1995
124   The heat equation shrinks embedded plane curves to round poi.. (context) - Grayson - 1989
114   Level Set Methods: Evolving Interfaces in Geometry (context) - Sethian - 1996
114   Generalized Solutions of Hamilton-Jacobi Equations (context) - Lions - 1982
91   A variational level set approach to multiphase motion - Zhao, Chan et al. - 1996
83   A fast marching level set method for monotonically advancing.. - Sethian - 1996
57   Guaranteed-quality mesh generation for curved surfaces (context) - Chew - 1993
55   Curvature and the evolution of fronts (context) - Sethian - 1985
51   Two approximations of solutions of Hamilton-Jacobi equations (context) - Crandall, Lions - 1984
48   Guaranteed-quality triangular meshes (context) - Chew - 1989
44   cient implementation of essentially nonoscillatory shock-cap.. (context) - Shu, Osher - 1988
34   and Applications of Level Set Methods for Propagating Interf.. (context) - Sethian, Algorithms - 1995
31   Numerical algorithms for propagating interfaces: Hamilton-Ja.. (context) - Sethian - 1990
30   Some relations between nonexpansive and order preserving map.. (context) - Crandall, Tartar - 1980
25   Parallel automated adaptive procedures for unstructured mesh.. - Shephard - 1995
22   A unied level set approach to etching (context) - Adalsteinsson, Sethian - 1997
22   A unied level set approach to etching (context) - Adalsteinsson, Sethian - 1995
22   A unied level set approach to etching (context) - Adalsteinsson, Sethian - 1995
16   Numerical Solution of Partial Di erential Equations by the F.. (context) - Johnson - 1987
12   Numerical schemes for conservation laws via Hamilton-Jacobi .. (context) - Corrias, Falcone et al. - 1995
10   Numerical simulation of shock interaction with complex geome.. (context) - ohner, Baum - 1990
6   Numerical discretization of the rst-order hamilton-jacobi eq.. (context) - Abgrall - 1996
5   Convergence of MUSCL and ltered schemes for scalar conservat.. (context) - Lions, Souganidis - 1995
4   Adaptive level set methods interfaces (context) - Milne - 1995
3   A new and simple algorithm for quality two-dimensional mesh .. (context) - Ruppert - 1992
3   Compact advection schemes on unstructured grids (context) - Deconinck, Struijs et al. - 1993
3   upwind advection on a triangular mesh (context) - Roe - 1990
3   Linear advection schemes on triangular meshes (context) - Roe - 1987
1   Technical Report CSL (context) - Bern, Epstein et al. - 1992
1   First order quasilinear equations in independent variables (context) - Kruzkov - 1970
1   omputing minimal surfaces via level set curvature ow (context) - Chopp - 1993



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Motion by Intrinsic Laplacian of Curvature - Chopp, Sethian (1999)   (Correct)
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