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Mesh, Geometric Modeling and Numerical Simulation, Volume 2: Metrics and Meshes, Adaptation and Applications

Mesh, Geometric Modeling and Numerical Simulation, Volume 2: Metrics and Meshes, Adaptation and Applications

Houman Borouchaki, Paul Louis George

ISBN: 978-1-786-30117-8

Dec 2018, Wiley-ISTE

400 pages

Select type: Hardcover

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Description

This book (composed of 2 volumes) introduces the notions and concepts at the basis of geometric modeling problems, triangulation and mesh in the application framework numerical simulations. First, the basic geometric elements, seen as interpolating from Lagrange or Bezier, are described. Then various problems related to triangulations and geometric modeling are addressed, in order to go from a continuous model to a discrete model and vice versa. The notion of metric is introduced and discussed, metrics being the natural way to assess the quality of geometric elements and triangulations as well as the precision of interpolating. Triangulation and metric make it possible to define the concept of mesh. The methods of construction and mesh optimization are discussed before addressing the issue of adaptation mesh and its application in numerical simulations. Some useful formulas and algorithms supplement and illustrate the methodologies introduced.
Chapter 1. Introduction
Chapter 2. Mesh of a Curve
Chapter 3. Simplicial Mesh
Chapter 4. Non Simplicial Mesh
Chapter 5.  The Building of high degree Mesh
Chapter 6 Mesh Optimization
Chapter 7. Mesh Adaptation
Chapter 8. Parallelization
Chapter 9. Applications
Chapter 10. A few algorithms and formulas
Chapter 11. Conclusions and perspectives