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

JA Sethian, A Vladimirsky - Proceedings of the National …, 2000 - National Acad Sciences
JA Sethian, A Vladimirsky
Proceedings of the National Academy of Sciences, 2000National Acad Sciences
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 Rn and on manifolds and connections to more general static …
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 Rn and on manifolds and connections to more general static Hamilton–Jacobi equations.
National Acad Sciences
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