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

نویسندگان

  • E. Carlini
  • M. Falcone
  • N. Forcadel
  • R. Monneau
چکیده

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 time-dependent velocity without 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. AMS Classification: 65M06, 65M12, 49L25.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign

We present a new Fast Marching algorithm for an eikonal equation with a velocity changing sign. This first order equation models a front propagation in the normal direction. The algorithm is an extension of the Fast Marching Method in two respects. The first is that the new scheme can deal with a time-dependent velocity and the second is that there is no restriction on its change in sign. We an...

متن کامل

Comparison Principle for a Generalized Fast Marching Method

In [4], 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 [4] for which we state a general comparison principle. We also prove the conver...

متن کامل

FEM-like Fast Marching Method for the Computation of the Boat-Sail Distance and the Associated Voronoi Diagram

A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, ...

متن کامل

Prestack first-break traveltime tomography using the double-square-root eikonal equation

Traveltime tomography with shot-based eikonal equation fixes shot positions then relies on inversion to resolve any contradicting information between independent shots and achieve a possible cost-function minimum. On the other hand, the double-square-root (DSR) eikonal equation that describes the whole survey, while providing the same first-arrival traveltimes, allows not only the receivers but...

متن کامل

An Efficient Solution to the Eikonal Equation on Parametric Manifolds

We present an efficient solution to the eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applicati...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006