A PDE-based fast local level set method

We develop a fast method to localize the level set method of Osher and Seth ian (1988, J. Comput. Phys. 79, 12) and address two important issues that a re intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance function to the interf ace efficiently without appreciably moving the interface. This fast local l evel set method reduces the computational effort by one order of magnitude, works in as much generality as the original one, and is conceptually simpl e and easy to implement. Our approach differs from previous related works i n that we extract all the information needed from the level set function (o r functions in multiphase flow) and do not need to find explicitly the loca tion of the interface in the space domain. The complexity of our method to do tasks such as extension and distance reinitialization is O (N), where N is the number of points in space, not O(N log N) as in works by Sethian (19 96, Proc. Not. Acad. Sci. 93, 1591) and Helmsen and co-workers (1996, SPIE Microlithography IX, p. 253). This complexity estimation is also valid for quite general geometrically based front motion for our localized method. (C ) 1999 Academic Press.