The goal of this book is to promote the use of level set methods by the many scientists and engineers working on moving interface problems. The authors provide some motivational/intuitive background on the scope and variety of moving interface problems and their mathematical formulation. They also review the pros and cons of traditional numerical techniques. The bulk of the book addresses the foundation of essential mathematical and numerical methods necessary for applying the level set method, with particular emphasis on problems in which the interface is just one part of a more complicated physical system. The book concludes with a few select example applications drawn from the authors' research. The book is intended for students and researchers interested in computation in the physical sciences, i.e.engineers, computational fluid dynamicists and applied mathematicians who want to use these methods for their own computations. It is suitable for use in a graduate level course on numerical methods, as a users guide to applying the methods, and as a general reference for mathematics related to level sets and the numerical solution of equations of ''Hamiltonian-Jacobi'' type.

Table of Contents:
Implicit Surfaces.- Implicit Functions.- Signed Distance Functions.- Level Set Methods.- Motion in an Externally Generated Velocity Field.- Motion Involving Mean Curvature.- Hamilton-Jacobi Equations.- Motion in the Normal Direction.- Constructing Signed Distance Functions.- Extrapolation in the Normal Direction.- Particle Level Set Method.- Codimension-Two Objects.- Image Processing and Computer Vision.- Image Restoration.- Snakes, Active Contours, and Segmentation.- Reconstruction of Surfaces from Unorganized Data Points.- Computational Physics.- Hyperbolic Conservation Laws and Compressible Flow.- Two-Phase Compressible Flow.- Shocks, Detonations, and Deflagrations.- Solid-Fluid Coupling.- Incompressible Flow.- Free Surfaces.- Liquid-Gas Interactions.- Two-Phase Incompressible Flow.- Low-Speed Flames.- Heat Flow.