Level Set Methods And Fast Marching Methods - Evolving Interfaces In Computational Geometry, Fluid Mechanics, Computer Vision, And Materials Science - Sethian James

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Résumé :
This book is 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. They rely on a fundamental shift in how one views moving boundaries, rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. The resulting numerical techniques can be used to track three-dimensional complex fronts that can develop sharp corners and change topology as they evolve. This new edition of Professor Sethian's successful text includes the latest advances in fast marching methods and extends the original volume to cover new areas of application. The book begins with an introduction to the dynamics of moving curves and surfaces. Next, efficient computational techniques for approximating viscosity solutions to partial differential equations are developed, using the numerical technology from hyperbolic conservation laws. A large collection of applications are given, including examples from physics, chemistry, fluid mechanics, combustion, image processing, materials science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal 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.

Biographie:
James Sethian received his Ph.D. in mathematics from the University of California, Berkeley, where he is now a full professor.