Comparison principle for a Generalized Fast Marching Method

Nicolas Forcadel (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems

In \cite{CFFM06}, the authors have proposed a generalization of the classical Fast Marching Method of Sethian for the eikonal equation in the case where the normal velocity depends on space and time and can change sign. The goal of this paper is to propose a modified version of the Generalized Fast Marching Method proposed in \cite{CFFM06} for which we state a general comparison principle. We also prove the convergence of the new algorithm.

Mots clés: convergence; Eikonal equation; fast marching scheme; monotone scheme

Domaines: Analyse numérique [math.NA]

Nicolas Forcadel. Comparison principle for a Generalized Fast Marching Method. SIAM Journal on Numerical Analysis, 2009, 47 (3), pp. 1923-1951. ⟨hal-00266075⟩