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Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science

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ISBN-10: 0521645573

ISBN-13: 9780521645577

Edition: 2nd 1999 (Revised)

Authors: J. A. Sethian

List price: $69.99
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This text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings.
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Book details

List price: $69.99
Edition: 2nd
Copyright year: 1999
Publisher: Cambridge University Press
Publication date: 6/13/1999
Binding: Paperback
Pages: 404
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 1.540
Language: English

Preface to the Second Edition
Equations of Motion for Moving Interfaces
Formulation of Interface Propagation
A boundary value formulation
An initial value formulation
Advantages of these perspectives
A general framework
A look ahead/A look back
A larger perspective
Theory and Algorithms
Theory of Curve and Surface Evolution
Fundamental formulation
Total variation: stability and the growth of oscillations
The role of entropy conditions and weak solutions
Effects of curvature
Viscosity Solutions and Hamilton-Jacobi Equations
Viscosity solutions of Hamilton-Jacobi equations
Some additional comments and references
Traditional Techniques for Tracking Interfaces
Marker/string methods
Volume-of-fluid techniques
Constructing an approximation to the gradient
Hyperbolic Conservation Laws
The linear wave equation
The non-linear wave equation
Basic Algorithms for Interface Evolution
Convergence of schemes for Hamilton-Jacobi equations
Hyperbolic schemes and Hamilton-Jacobi equations
The example of a propagating one-dimensional graph
The initial value problem: the Level Set Method
The boundary value problem: the stationary method
Schemes for non-convex speed functions
Approximations to geometric variables
Calculating additional quantities
Computational domain boundary conditions
Putting it all together
Efficiency, Adaptivity, and Extensions
Efficient Schemes: the Narrow Band Level Set Method
Parallel algorithms
Adaptive mesh refinement
Narrow banding and fast methods
Details of the Narrow Band implementation
Efficient Schemes: Fast Marching Methods
The update procedure for the Fast Marching Method
Heap sorts and computational efficiency
Initial conditions
Network path algorithms
Optimal orderings
Higher accuracy Fast Marching Methods
Non-uniform orthogonal grids
General static Hamilton-Jacobi equations
Some clarifying comments
Triangulated Versions of Level Set Methods
Fundamentals and notation
A monotone scheme for H ([down triangle, open]u)
A positive scheme for homogeneous H ([down triangle, open]u)
A Petrov-Galerkin formulation
Time integration schemes
Schemes for curvature flow
Mesh adaptivity
Triangulated Fast Marching Methods
The update procedure
A scheme for a particular triangulated domain
Fast Marching Methods on triangulated domains
Constructing Extension Velocities
The need for extension velocities
Various approaches to extension velocities
Equations for extension velocities
Building extension velocities
A quick demonstration
Tests of Basic Methods
The basic Cartesian Level Set Method
Triangulated Level Set Methods for H-J equations
Accuracy of Fast Marching Methods
Tests of extension velocity methodology
Building Level Set and Fast Marching Applications
Statement of problem
Equations of motion
Flows under more general metrics
Volume-preserving flows
Motion under the second derivative of curvature
Triple points: variational and diffusion methods
Grid Generation
Statement of problem
Equations of motion
Results, complications, and future work
Image Enhancement and Noise Removal
Statement of problem
Equations of motion
Related work
Computer Vision: Shape Detection and Recognition
Shape detection/recovery
Surface evolution and the stereo problem
Reconstruction of obstacles in inverse problems
Shape recognition
Combustion, Solidification, Fluids, and Electromigration
Crystal growth and dendritic solidification
Fluid mechanics
Additional applications
Void evolution and electromigration
Computational Geometry and Computer-aided Design
Voronoi diagrams
Curve flows with constraints
Minimal surfaces and surfaces of prescribed curvature
Extensions to surfaces of prescribed curvature
Boolean operations on shapes
Extracting and combining two-dimensional shapes
Shape smoothing
Optimality and First Arrivals
Optimal path planning
Constructing shortest paths on weighted domains
Constructing shortest paths on manifolds
Seismic traveltimes
Aircraft collision avoidance using Level Set Methods
Visibility evaluations
Etching and Deposition in Microchip Fabrication
Physical effects and background
Equations of motion for etching/deposition
Additional numerical issues
Two-dimensional results
Three-dimensional simulations
Validation with experimental results
Summary/New Areas/Future Work