Advancing Interfaces: Level Set and Fast Marching Methods

In this article, we review past work on Level Set Methods, introduced by Osher and Sethian in [20], and Fast Marching Methods, introduced by Sethian in [25], for tracking propagating interfaces in two and three space dimensions. Both sets of techniques are based on a partial differential equations view of interface motion, and rely on the use of the theory of viscosity solutions, upwind finite difference schemes for hyperbolic conservation laws, and the theory of curve and surface evolution developed in [23]. Both sets of techniques require an adaptive methodology to obtain computational efficiency. We briefly review some of these methods, and show some examples of some applications.