Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials ScienceThis book is an introduction to level set methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings. The numerical techniques can be used to track three-dimensional complex fronts that can develop sharp corners and change topology as they evolve. A large collection of applications are provided in the text, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision and control theory.This book will be a useful resource for mathematicians, applied scientists, practicing engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces. |
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Page viii
... schemes for Hamilton - Jacobi equations 60 Hyperbolic schemes and Hamilton - Jacobi equations 61 The example of a ... scheme for homogeneous H ( Vu ) 109 9.4 A Petrov - Galerkin formulation 112 9.5 Time integration schemes 113 9.6 ...
... schemes for Hamilton - Jacobi equations 60 Hyperbolic schemes and Hamilton - Jacobi equations 61 The example of a ... scheme for homogeneous H ( Vu ) 109 9.4 A Petrov - Galerkin formulation 112 9.5 Time integration schemes 113 9.6 ...
Page ix
... scheme for a particular triangulated domain 10.3 Fast Marching Methods on triangulated domains 121 123 11 Constructing Extension Velocities 127 11.1 The need for extension velocities 127 11.2 Various approaches to extension velocities ...
... scheme for a particular triangulated domain 10.3 Fast Marching Methods on triangulated domains 121 123 11 Constructing Extension Velocities 127 11.1 The need for extension velocities 127 11.2 Various approaches to extension velocities ...
Page xvi
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Page xviii
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Page xx
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Contents
III | xv |
IV | xx |
V | 10 |
VI | 26 |
VIII | 41 |
IX | 43 |
X | 67 |
XII | 86 |
XXII | 133 |
XXV | 157 |
XXVI | 178 |
XXVII | 204 |
XXX | 231 |
XXXII | 248 |
XXXIV | 277 |
XXXVI | 321 |
Other editions - View all
Level Set Methods and Fast Marching Methods: Evolving Interfaces in ... James Albert Sethian No preview available - 1999 |
Common terms and phrases
adaptive mesh refinement algorithm applications approach approximation Band Level Set boundary conditions boundary value calculation cells Chapter compute conservation laws consider construct convex curvature flow curve deposition discussed domain Eikonal equation entropy entropy condition equations of motion etching evaluate evolution evolving example extension velocity Fast Marching Method Fext flame fluid formulation front propagation function F geometric given goal gradient grid points H(Vu Hamilton-Jacobi equation Hamiltonian heat equation hyperbolic conservation laws interface level set equation level set function Level Set Methods mean curvature mesh Min/Max flow moving Narrow Band Level noise non-convex normal direction numerical order scheme partial differential equation particles positive re-deposition re-initialization region second order Sethian shape shortest path shows signed distance function simulations smooth solving speed F speed function step sticking coefficient straightforward techniques term three-dimensional tion triangulated two-dimensional UNDEF update upwind velocity field viscosity solution weak solution zero level set