Motion of curves in three spatial dimensions using a level set approach

The level set method was originally designed for problems dealing with codi mension one objects. where it has been extremely succesful. especially when topological changes in the interface, i.e., merging and breaking, occur. A ttempts have been made to modify it to handle objects of higher codimension , such as vortex filaments, while preserving the merging and breaking prope rty. We present numerical simulations of a level set based method for movin g curves in R-3. the model problem for higher codimension, that allows for topological changes. A vector valued level set function is used with the ze ro level set representing the curve. Our results show that this method can handle many types of curves moving under all types of geometrically based f lows while automatically enforcing merging and breaking. (C) 2001 Academic Press.