Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids
Journal of Computational Physics
A level set projection model of lipid vesicles in general flows
Journal of Computational Physics
Simulations of a stretching bar using a plasticity model from the shear transformation zone theory
Journal of Computational Physics
A Generalized Fast Marching Method for Dislocation Dynamics
SIAM Journal on Numerical Analysis
Simulating free surface flow with very large time steps
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Simulating free surface flow with very large time steps
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A localized re-initialization equation for the conservative level set method
Journal of Computational Physics
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The level set method [S. Osher and J. A. Sethian, J. Comput. Phys., 79 (1988), pp. 12-49] has become a widely used numerical method for moving interfaces; e.g., see the many examples in [J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Science, Cambridge University Press, London, 1996; S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer Verlag, Heidelberg, 2002]. For many applications, the velocity of the interface is known only on the interface, while the level set method requires information about the interface speed at least in a neighborhood of grid points near the interface. To address this issue, velocity extensions are used to map the velocity information on the interface into the rest of the computational domain [D. Adalsteinsson and J. Sethian, J. Comput. Phys., 118 (1995), pp. 269-277]. This allows the level set method to proceed. The velocity extension method presented in [D. Adalsteinsson and J. Sethian, J. Comput. Phys., 118 (1995), pp. 269-277] uses the fast marching method [J. Sethian, Proc. Natl. Acad. Sci., 93 (1996), pp. 1591-1595; J. Sethian, SIAM Rev., 41 (1999), pp. 199-235], and is only a first-order approximation for the velocity field near the interface. Furthermore, it can lead to unexpected behavior in some cases. This is primarily due to the strictly local solution for the characteristics of the flow near the interface. In this paper, we look more closely at the characteristics near the interface, and then present a modified velocity extension method, also based on the fast marching method, which handles the characteristcs more accurately. In turn, this new method will lead to some interesting new possibilities for the fast marching method.