Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

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An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals (2006, methodology): “Therefore, in synthetic experiment the boundary measurements can be obtained by solving the equation (2.1) directly using the Fast Sweeping Method together with the exact velocity c.”
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.”
3D distance fields: a survey of techniques and applications (2006, methodology): “proposed a fast sweeping method for more general hamiltonians based on LaxFriederichs rather than Godunov’s scheme [66].”
A fast sweeping method for Eikonal equations (2004, methodology): “The fast sweeping method has been extended to more general Hamilton-Jacobi equations [18, 12].”
An Optimal Control Approach to Sequential Machine Teaching (2018, methodology): “Numerical approaches for solving HJB include the fast-marching method (Tsitsiklis, 1995) and Lax–Friedrichs sweeping (Kao et al., 2004).”