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Meshing, Geometric Modeling and Numerical Simulation 1: Form Functions, Triangulations and Geometric Modeling

Meshing, Geometric Modeling and Numerical Simulation 1: Form Functions, Triangulations and Geometric Modeling

Houman Borouchaki, Paul Louis George

ISBN: 978-1-786-30038-6

Oct 2017

384 pages

In Stock

£120.00

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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. Finite elements and shape functions
Chapter 3. Lagrange and Bézier interpolation
Chapter 4. Geometrical elements and geometrical validity
Chapter 5. Triangulation
Chapter 6. Delaunay Triangulation
Chapter 7. Triangulation and Constraints
Chapter 8. Geometrical modeling
Chapter 9. Metric, definitions and proprieties
Chapter 10. Errors and metric interpolation
Chapter 11. Conclusions and perspectives
 Chapter 1. Introduction
Chapter 2. Finite elements and shape functions
Chapter 3. Lagrange and Bézier interpolation
Chapter 4. Geometrical elements and geometrical validity
Chapter 5. Triangulation
Chapter 6. Delaunay Triangulation
Chapter 7. Triangulation and Constraints
Chapter 8. Geometrical modeling
Chapter 9. Metric, definitions and proprieties
Chapter 10. Errors and metric interpolation
Chapter 11. Conclusions and perspectives