Fast methods for the Eikonal and related Hamilton- Jacobi equations on unstructured meshes.

By James A. Sethian, Alexander Vladimirsky. Proceedings of the National Academy of Sciences of the United States of America, 2000

345 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8de04bcafe1cb368f3df906d3b3bd89a2a806d02

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In Computational Mechanics

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Citations in the corpus

An efficient and parallel level set reinitialization method - Application to micromechanics and microstructural evolutions (2015, background): “obtuse) triangulations [11].”
Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms (2003, methodology): “Our derivation of such discretizations generalizes the approach used in defining the Fast Marching Method on unstructured meshes given in [38].”
Manitest: Are classifiers really invariant? (2015, background): “Unfortunately, for arbitrary anisotropic metrics, consistency is however not guaranteed, and the exact computation of the geodesics becomes much more difﬁcult and computationally demanding (see [2, 23, 25, 27]).”
Path Planning for Autonomous Underwater Vehicles (2007, methodology): “The output is a net of vertices linked to their neighbors by edges, see figure 13. Versions of breadth-first and Fast Marching algorithms on this kind of unstructured mesh [ 36 ] are implemented in the following section.”
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model (2008, methodology): “The fast marching method [23, 24, 25] and the fast sweeping method [26, 27, 28, 29] are designed to solve a nonlinear discretized system directly and efficiently by exploiting the causality of the Eikonal equations.”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, methodology): “We also note that in recent work, Sethian and Vladimirsky have been able to produce general schemes for non-Eikonal anisotropic general optimal control problems with the same computational complexity as these Dijkstra-like methods; for details, see [23, 24].”
MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains (2007, methodology): “The FMM [2], [18], [19], [20] combines entropy-satisfying upwind schemes and a fast sorting technique to find the solution in one-pass algorithm.”
Numerical methods for shape-from-shading: A new survey with benchmarks (2008, methodology): “Other acceleration techniques for the eikonal equation can be found in [94,95] where the so-called \fast marching method" is described.”
Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations (2003, methodology): “In [21, 22], the authors provide an ordered upwind method to solve a general class of static Hamilton-Ja cobi equations.”
Level set topology optimization of structures under stress and temperature constraints (2020, methodology): “The boundary of the structure is changed under a given velocity field VnðxÞ using the following Hamilton–Jacobi equation [19]”
Computer Methods and Programs in Biomedicine (neutral): “On the other hand, FMM schemes such as those presented in [198–200] can be used to deal with anisotropic M .”