Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations

Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-jacob1 Formulations

Effect of initial conditions on the speed of reaction-diffusion fronts.

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is a...

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Level set methods [Osher and Sethian. Fronts propagating with curvaturedependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tre...

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conserv...

Lower Bound Gradient Estimates for First-order Hamilton-jacobi Equations and Applications to the Regularity of Propagating Fronts

This paper is concerned with rst-order time-dependent Hamilton-Jacobi Equations. Exploiting some ideas of Barron and Jensen 9], we derive lower bound estimates for the gradient of a locally Lipschitz continuous viscosity solution u of equations with a convex Hamiltonian. Using these estimates in the context of the level-set approach to front propagation, we investigate the regularity properties...