Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms

By James A. Sethian, Alexander Vladimirsky. SIAM Journal on Numerical Analysis, 2003

432 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/332f4f9c7bac9c288481f0ef8f094be3cf1bc8aa

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

A Survey of Methods for Computing (un)Stable Manifolds of Vector Fields (2005, methodology): “Ordered Upwind Methods (OUMs) were originally introduced for static Hamilton-JacobiBellman PDEs [Sethian & Vladimirsky, 2003].”
Image-guided Blended Neighbor Interpolation of Scattered Data (2009, methodology): “Other suitable algorithms include variants of fast-marching methods (Sethian, 1999; Sethian and Vladimirsky, 2005; Konukoglu et al., 2007) and sweeping methods (Tsai et al., 2003; Qian et al., 2007), but care must be taken to handle correctly the anisotropic and inhomogeneous coefficients D(x) in…”
Manitest: Are classifiers really invariant? (2015, background): “The extension to arbitrary dimensions is straightforward, and we refer to [26, 28] for more complete explanations and computations.”
Shape From Shading (2006, neutral): “In particular in [40], Sethian and Vladimirsky prove that the numerical solutions computed by the fast marching/ordered upwind methods converge toward the continuous viscosity solution (with Dirichlet boundary data on the boundary of the image).”
Path Planning for Autonomous Mobile Robots: A Review (2021, methodology): “FMM produces sub-optimal results if used with direction-dependent (anisotropic) costs [215].”
MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains (2007, neutral): “For anisotropic FMM, see [34].”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, neutral): “Numerical approximations of this function can be computed iteratively for general nonlinear dynamics with two competing inputs [15], or for restricted classes of dynamics by fast iterative [16] and even noniterative [17], [18] schemes.”
On anelliptic approximations for qP velocities in VTI media (2004, methodology): “For a more accurate and robust extension of the fast marching method for anisotropic traveltime calculation, the ordered upwind methods of Sethian and Vladimirsky (2001, 2003) are recommended.”
A Toolbox of Level Set Methods (2005, methodology): “A variety of di erent algorithms have been proposed for approximating minimum time to reach, cost to go or general stationary HJ PDE solutions for systems with inputs and nonlinear dynamics [3,11,29,36].”