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The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O ( M log M ) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in R n and on manifolds and connections to more general static Hamilton–Jacobi equations.
Sethian et al. (Tue,) studied this question.