Motion of Multiple Junctions: A Level Set Approach

Abstract

A coupled level set method for the motion of multiple junctions is proposed. The new method extends the "Hamilton-Jacobi" level set formulation of Osher and Sethian. It retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front. The diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature-dependent speed. Systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature-dependent motion.