Fast methods for the Eikonal and related Hamilton– Jacobi equations on unstructured meshes
2000; National Academy of Sciences; Volume: 97; Issue: 11 Linguagem: Inglês
10.1073/pnas.090060097
ISSN1091-6490
AutoresJames A. Sethian, Alexander Vladimirsky,
Tópico(s)Markov Chains and Monte Carlo Methods
ResumoThe 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.
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