Convergence of a Generalized Fast Marching Method for a non-convex eikonal equation

Elisabetta Carlini (1) , Maurizio Falcone (1) , Nicolas Forcadel (2) , Régis Monneau (2)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We present a new Fast Marching algorithm for a non-convex eikonal equation modeling front evolutions in the normal direction. The algorithm is an extension of the Fast Marching Method since the new scheme can deal with a \emph{time-dependent} velocity without \emph{any restriction on its sign}. We analyze the properties of the algorithm and we prove its convergence in the class of discontinuous viscosity solutions. Finally, we present some numerical simulations of fronts propagating in $\R^2$.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Elisabetta Carlini, Maurizio Falcone, Nicolas Forcadel, Régis Monneau. Convergence of a Generalized Fast Marching Method for a non-convex eikonal equation. SIAM Journal on Numerical Analysis, 2008, 46 (6), pp. 2920-2952. ⟨hal-00109596⟩