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 numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between the meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this meshing vision.
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About the Author
Paul-Louis George, French Institute for Research in Computer Science and Automation, France.
Table of ContentsChapter 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
1. Finite Elements and Shape Functions.
2. Lagrange and Bézier Interpolants.
3. Geometric Elements and Geometric Validity.
5. Delaunay Triangulation.
6. Triangulation and Constraints.
7. Geometric Modeling: Methods.
8. Geometric Modeling: Examples.
9. A Few Basic Algorithms and Formulae.