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Meshing, Geometric Modeling and Numerical Simulation 3

Release Date: 2020/12/01
ISBN: 9781786306098
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Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena.

In Volume 1, the theoretical foundations relating to triangulations, finite element shape functions and their interpretations as geometric patches were explored. This has made it possible to build tools that make the geometric modeling of any object possible. These elements are used in Volume 2 to treat meshing problems in their different implementations.

Meshing, Geometric Modeling and Numerical Simulation 3 offers technical additions to the methods seen in the first two volumes and a significant portion of this book is dedicated to mesh visualization problems and solutions, especially those with a high degree of complexity.

Table of Contents

  1. Cover
  2. Title page
  3. Copyright
  4. Foreword
  5. Introduction
  6. Chapter 1. Data and Basic Techniques
    1. 1.1. Basic data structures and basic techniques
    2. 1.2. Internal data structures
    3. 1.3. External data structures
    4. 1.4. Data structures and memory access
  7. Chapter 2. Mesh Transformations, Patching, Merging and Immersion
    1. 2.1. Geometric transformations
    2. 2.2. Reconnection
    3. 2.3. Merging
    4. 2.4. Immersion
  8. Chapter 3. Renumbering and Memory
    1. 3.1. Vertex and node renumbering
    2. 3.2. Renumbering of the elements
    3. 3.3. Some examples
  9. Chapter 4. High-Degree Mesh Visualization
    1. 4.1. Geometric operators and topological operators
    2. 4.2. Representation of curved meshes
    3. 4.3. Quick introduction to OpenGL and to the design of a graphics software program
    4. 4.4. Some examples
  10. Chapter 5. Visualization of a Solution Field Related to a High-Degree Mesh
    1. 5.1. Element recursive subdivision
    2. 5.2. Recursive subdivision of a solution field
    3. 5.3. Classic or adaptive tessellation
    4. 5.4. Toward the design of graphic software based on OpenGL
    5. 5.5. Some examples
  11. Chapter 6. Meshes and Finite Element Calculations
    1. 6.1. From continuous formulation to discrete notation
    2. 6.2. Calculation of an elementary matrix
    3. 6.3. Matrix or right-hand side assembly
  12. Chapter 7. Meshes and Finite Volume Calculation
    1. 7.1. Presentation of the finite volume method with a first-order problem
    2. 7.2. Finite volume methods for two-dimensional Euler equations
    3. 7.3. From theory to practice
    4. 7.4. Numerical examples
  13. Chapter 8. Examples Through Practice
    1. 8.1. Reading, writing and manipulating a mesh
    2. 8.2. Programming a hashing algorithm
    3. 8.3. One point insertion operator per cavity, application to image compression
    4. 8.4. Retrieving a connected component
    5. 8.5. Exercises on metrics
  14. Chapter 9. Some Algorithms and Formulas
    1. 9.1. Bernstein polynomials and Bézier forms
    2. 9.2. Localization problems in a curved mesh
    3. 9.3. Space-filling curves
  15. Conclusion and Perspectives
  16. Bibliography
  17. Index
  18. End User License Agreement
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