Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations

By Yen-Hsi Richard Tsai, Li-Tien Cheng, Stanley J. Osher, Hongkai Zhao. SIAM Journal on Numerical Analysis, 2003

490 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0cbb291dab9af8680df6b2b8d3218b85b3fcbb1a

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Stress-based topology optimization using an isoparametric level set method (2012, methodology): “Here we use an implementation of the fast sweeping method [16–18].”
Level set methods: an overview and some recent results (2001, background): “See [85] for details, which also include results for a number of nonconvex Hamiltonians.”
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations (2004, methodology): “[20] combined such a Gauss–Seidel type iteration method with the monotone upwind Godunov Hamiltonian [1,10], and the resulting algorithm is very easy to implement and accurate.”
A fast sweeping method for Eikonal equations (2004, methodology): “The fast sweeping method has been extended to more general Hamilton-Jacobi equations [18, 12].”
Multiple level set methods with applications for identifying piecewise constant functions (2004, methodology): “There are dierent methods available in the literature for reinitialize the level set functions, see [36, 44, 43, 50 , 52].”
Image-guided Blended Neighbor Interpolation of Scattered Data (2009, methodology): “Image-guided blended neighbor interpolation of scattered data”
A binary level set model and some applications to Mumford-Shah image segmentation (2006, methodology): “Based on (8), Chan and Vese [2] proposed the following minimization problem for a two-phase segmentation (9) Here, is the level set function satisfying (1), is the Heaviside function: if and if , and is the Dirac-delta function which by definition only collects the zero level set of .”
MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains (2007, methodology): “TheFSM[17],[21],[22],[23],[24],[25]isaniterative algorithm with optimal complexity that finds the numerical solution by using a nonlinear upwind method and Gauss-Seidel type iterations with alternating sweepings in pre-determined directions.”
Continuum crowds (2006, methodology): “However, efficient methods have been developed to solve this type of equation, notably the fast marching method [Tsitsiklis 1995] and the fast sweeping method [Tsai et al. 2005].”