Level Set Methods and Dynamic Implicit Surfaces

Stanley Osher, Ronald Fedkiw

286 pages, parution le 17/12/2002

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Résumé

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.

Contents

Part I: Implicit Surfaces

Implicit Functions
Signed Distance Functions

Part II: 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

Part III: Image Processing and Computer Vision

Image Restoration
Snakes, Active Contours and Segmentation
Reconstruction of Surfaces from Unorganized Data Points

Part IV: 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

L'auteur - Stanley Osher

Unversity of California, Los Angeles, CA, USA

L'auteur - Ronald Fedkiw

University of Stanford, CA, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Stanley Osher, Ronald Fedkiw
Parution	17/12/2002
Nb. de pages	286
Format	16 x 24
Couverture	Relié
Poids	596g
Intérieur	Noir et Blanc
EAN13	9780387954820
ISBN13	978-0-387-95482-0