Journal of Computational Physics
A Discontinuous Spectral Element Method for the Level Set Equation
Journal of Scientific Computing
A coupled quadrilateral grid level set projection method applied to ink jet simulation
Journal of Computational Physics
Journal of Computational Physics
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
A study of numerical methods for the level set approach
Applied Numerical Mathematics
Journal of Computational Physics
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
Journal of Computational Physics
A gradient-augmented level set method with an optimally local, coherent advection scheme
Journal of Computational Physics
Journal of Computational Physics
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Marker Redistancing/Level Set Method for High-Fidelity Implicit Interface Tracking
SIAM Journal on Scientific Computing
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
A level set projection model of lipid vesicles in general flows
Journal of Computational Physics
Journal of Computational Physics
Simulations of a stretching bar using a plasticity model from the shear transformation zone theory
Journal of Computational Physics
Applied Numerical Mathematics
Analysis and applications of the Voronoi Implicit Interface Method
Journal of Computational Physics
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A parallel fast sweeping method for the Eikonal equation
Journal of Computational Physics
A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows
Journal of Computational Physics
A gradient augmented level set method for unstructured grids
Journal of Computational Physics
A level set two-way wave equation approach for Eulerian interface tracking
Journal of Computational Physics
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The fast marching method published by Sethian [Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 1591--1595] is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic. It has been used in a wide variety of applications such as robotic path planning [R. Kimmel and J. Sethian, Fast Marching Methods for Computing Distance Maps and Shortest Paths, Tech. Report 669, CPAM, University of California, Berkeley, 1996], crack propagation [M. Stolarska et al., Modelling crack growth by level sets in the extended finite element method, Comput. Methods Appl. Mech. Engrg., to appear; Internat. J. Numer. Methods Engrg., 51 (2001), pp. 943--960; N. Sukumar, D. L. Chopp, and B. Moran, Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, J. Comput. Phys., submitted], seismology [J. Sethian and A. Popovici, Geophysics, 64 (1999), pp. 516--523], photolithography [J. Sethian, Fast marching level set methods for three-dimensional photolithography development, in Proceedings of the SPIE 1996 International Symposium on Microlithography, Santa Clara, CA, 1996], and medical imaging [R. Malladi and J. Sethian, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 9389--9392]. It has also been a valuable tool for the implementation of modern level set methods where it is used to efficiently compute the distance to the front and/or an extended velocity function.In this paper, we improve upon the second order fast marching method of Sethian [SIAM Rev., 41 (1999), pp. 199--235] by constructing a second order approximation of the interface generated from local data on the mesh. The data is interpolated on a single box of the mesh using a bicubic approximation. The distance to the front is then calculated by using a variant of Newton's method to solve both the level curve equation and the orthogonality condition for the nearest point to a given node. The result is a second order approximation of the distance to the interface which can then be used to produce second order accurate initial conditions for the fast marching method and a third order fast marching method.