Advances in Level Set and Related Methods: New Technology and Applications

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

NSF Proposal: DMS-0074735 "Advances in Level Set and Related Methods: New Technologies and Applications" Principal Investigator: Stanley J. Osher ABSTRACT The level set method devised by Osher and Sethian in 1988 has proven to be phenomenally successful as a numerical and theoretical device for representing and analyzing the motion of curves in R^2 and surfaces in R^3. A level set calculus has been developed, and recent extensions include the ghost fluid method, convolution generated motion, dynamic surface extension, the variational level set approach, and the motion of higher codimensional objects. Recent applications include multiphase fluid dynamics, the island dynamics model for epitaxial growth, level set based interpolation of unorganized points, and fast methods in image restoration. This work was partially supported by our previous NSF grants. The goal of this proposed research is to extend the technology and the range of applications through the following two projects: (1) Convolution generated motion for filaments. (2) Fast algorithms for steady state geometric Hamilton-Jacobi equations and the induced motion of fronts. The level set method is rapidly becoming the method of choice to simulate on the computer a host of important physical, biological, materials science, image processing, computer vision, electromagnetic and other real world problems. In particular areas of nanotechnology will also be impacted. Improvements of the numerical methods used to simulate these phenomena will ultimately be crucial in the design of computer chips, analysis of explosions, recognition of objects and many other areas of modern technology. This proposal addresses further improvements of the level set and related methods.