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.
These mesh adaptations are generally governed by a posteriori error estimators representing an increase of the error with respect to a size or metric. Independently of this metric of calculation, compliance with a geometry can also be calculated using a so-called geometric metric. The notion of mesh thus finds its meaning in the metric of its elements.
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.
Houman Borouchaki is Professor at the University of Technology of Troyes (UTT) in France. He has been conducting research on mesh-related issues for more than 30 years, and is the author of several pieces of meshing software used in industry.
Paul-Louis George is Research Director at the French Institute for Research in Computer Science and Automation (Inria). The author of several books on meshes, he is today considered the father of mesh in France. He is one of the authors of the volume meshing software GHS3D integrated in most CAD systems.
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