Abstract
We summarize recent advances in level set methods and Fast Marching Methods for propagating interfaces, which are computational techniques for tracking evolving fronts in two and three space dimensions. Here, we review the interconnection between the two techniques, discuss the recent extension of level set techniques to triangulated unstructured meshes, and provide a few examples of these techniques.
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References
Adalsteinsson, D., and Sethian, J.A., A Fast Level Set Method for Propagating Interfaces, J. Comp. Phys., 18 (2) (1995), 269–277.
Adalsteinsson, D., and Sethian, J.A., A Unified Level Set Approach to Etching, Deposition and Lithography I: Algorithms and Two-dimensional Simulations, 120 (1) (1995), 128–144.
Adalsteinsson, D., and Sethian, J.A., A Unified Level Set Approach to Etching,Deposition and Lithography II: Three-dimensional Simulations, 122 (2) (1995), 348–366.
Adalsteinsson, D., and Sethian, J.A., A Unified Level Set Approach to Etching,Deposition and Lithography III: Complex Simulations and Multiple Effects, J. Comp. Phys., 138 (1) (1997), 193–223.
Adalsteinsson, D., and Sethian, J.A., The Fast Construction of Extension Velocities in Level Set Methods, submitted for publication, J. Comp. Phys., (1997)
Barth, T.J., and Sethian, J.A., Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains, to appear, J. Comp. Phys., (1998)
Chang, Y.C., Hou, T.Y., Merriman, B., and Osher, S.J., A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows, Jour. Comp. Phys., 124 (1996), 449–464.
Chopp, D.L., Computing Minimal Surfaces via Level Set Curvature Flow, Jour. of Comp. Phys., 106(1993), 77–91.
Chopp, D.L., and Sethian, J.A., Flow Under Curvature: Singularity Formation, Minimal Surfaces, and Geodesics, Jour. Exper. Math., 2 (4) (1993), 235–255.
Crandall, M.G., and Lions, P-L., Viscosity Solutions of Hamilton—Jacobi Equations, Tran. AMS, 277 (1983), 1–43.
Kimmel, R., and Sethian, J.A., Fast Marching Methods on Triangulated Domains, submitted for publication, Proceedings of the National Academy of Sciences, March, 1998.
Kimmel, R., and Sethian, J.A., Application of Fast Marching Methods to Robotic Navigation and Construction of Optimal Paths, submitted for publication, IEEE Transactions on Robotics and Automation, 1996.
Malladi, R., and Sethian, J.A., An O(N log N) Algorithm for Shape Modeling, Proc. Nat. Acad. Sci., 93 (1996), 9389–9392.
Malladi, R., Sethian, J.A., and Vemuri, B.C., Shape Modeling with Front Propagation: A Level Set Approach, IEEE Trans. on Pattern Analysis and Machine Intelligence, 17 (2) (1995), 158–175.
Osher, S., and Sethian, J.A., Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton—Jacobi Formulation, Journal of Computational Physics, 79 (1988), 12–49.
Rhee, C., Talbot, L., and Sethian, J.A., Dynamical Study of a Premixed V flame, Jour. Fluid Mech., 300 (1995), 87 115.
Sethian, J.A., An Analysis of Flame Propagation, Ph.D. Dissertation, Dept. of Mathematics, University of California, Berkeley, CA, 1982.
Sethian, J.A., Curvature and the Evolution of Fronts, Comm. in Math. Phys., 101 (1985), 487–499.
Sethian, J.A., Numerical Methods for Propagating Fronts, in Variational Methods for Free Surface Interfaces, Eds. P. Concus and R. Finn, Springer-Verlag, NY, 1987.
Sethian, J.A., Curvature Flow and Entropy Conditions Applied to Grid Generation, J. Comp. Phys., 115 (1994), 440–454.
Sethian, J.A., A Fast Marching Level Set Method for Monotonically Advancing Fronts, Proc. Nat. Acad. Sci., 93 (4) (1996), 1591–1595.
Sethian, J.A., A Review of the Theory,Algorithms, and Applications of Level Set Methods for Propagating Interfaces, Acta Numerica, Cambridge University Press, 1996.
Sethian, J.A., Level Set Methods, Cambridge University Press, 1996.
Sethian, J.A., and Popovici, M., Three dimensional traveltimes computation using the Fast Marching Method, submitted for publication, Geophysics, 1997.
Sethian, J.A. and Strain, J.D., Crystal Growth and Dendritic Solidification J. Comp. Phys., 98 (1992), 231–253.
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Sethian, J.A. (1999). Advances in Fast Marching and Level Set Methods for Propagating Interfaces. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_36
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_36
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9744-0
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