Level Set Methods and Dynamic Implicit Surfaces (Applied Mathematical Sciences) 〈Vol.153〉

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Level Set Methods and Dynamic Implicit Surfaces (Applied Mathematical Sciences) 〈Vol.153〉

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  • 製本 Hardcover:ハードカバー版／ページ数 295 p.
  • 商品コード 9780387954820

Full Description

Scope, Aims, and Audiences This book, Level Set Methods and Dynamic Implicit Surfaces is designed to serve two purposes: Parts I and II introduce the reader to implicit surfaces and level set methods. We have used these chapters to teach introductory courses on the material to students with little more than a fundamental math background. No prior knowledge of partial di?erential equations or numerical analysis is required. These ?rst eight chapters include enough detailed information to allow students to create working level set codes from scratch. Parts III and IV of this book are based on a series of papers published by us and our colleagues. For the sake of brevity, a few details have been occasionally omitted. These chapters do include thorough explanations and enough of the signi?cant details along with the appropriate references to allow the reader to get a ?rm grasp on the material. This book is an introduction to the subject. We have given examples of the utility of the method to a diverse (but by no means complete) collection of application areas. We have also tried to give complete numerical recipes and a self-contained course in the appropriate numerical analysis. We - lieve that this book will enable users to apply the techniques presented here to real problems.

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.