Ordered upwind methods for static Hamilton–Jacobi equations

By James A. Sethian, Alexander Vladimirsky. Proceedings of the National Academy of Sciences of the United States of America, 2001

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LEVEL SET METHODS FOR FLUID INTERFACES (2003, methodology): “…see Kimmel & Sethian (1998) for an unstructured mesh version and Helmsen et al. (1996) for a comparison of a similar approach with volume-of-fluid techniques and Sethian & Vladimirsky (2001) for an extension of these Dijkstra-like ideas to anisotropic-front propagation and general optimal control.”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, result): “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].”
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 HJ equations.”
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations (2004, methodology): “For example, the ordered upwind method [18] updates the grid value using a minimization formula which essentially boils down to a version of Godunov type monotone schemes for convex and homogeneous Hamiltonians.”