Semi-Lagrangian methods for level set equations

A new numerical method for solving geometric moving interface problems is p resented. The method combines a level set approach and a semi-Lagrangian ti me stepping scheme which is explicit yet unconditionally stable. The combin ation decouples each mesh point from the others and the time step from the CFL stability condition, permitting the construction of methods which are e fficient, adaptive, and modular. Analysis of a linear one-dimensional model problem suggests a surprising convergence criterion which is supported by heuristic arguments and confirmed by an extensive collection of two-dimensi onal numerical results. The new method computes comet viscosity solutions t o problems involving geometry, anisotropy, curvature, and complex topologic al events. (C) 1999 Academic Press.