Meshing, Geometric Modeling and Numerical Simulation 2


Metrics, Meshes and Mesh Adaptation


Volume 2 – Geometric Modeling and Applications SET Coordinated by Marc Daniel

Meshing, Geometric Modeling and Numerical Simulation 2

Paul Louis George, French Institute for Research in Computer Science and Automation, France
Houman Borouchaki, University of Technology of Troyes, France
Frédéric Alauzet, French Institute for Research in Computer Science and Automation, France
Patrick Laug, French Institute for Research in Computer Science and Automation, France
Adrien Loseille, French Institute for Research in Computer Science and Automation, France
Loïc Maréchal, French Institute for Research in Computer Science and Automation, France


ISBN : 9781786301178

Publication Date : January 2019

Hardcover 408 pp

165.00 USD

Co-publisher

Description


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 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 vision of meshing.

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.

Contents


1. Metrics, Definitions and Properties.
2. Interpolation Errors and Metrics.
3. Curve Meshing.
4. Simplicial Meshing.
5. Non-simplicial Meshing.
6. High-order Mesh Construction.
7. Mesh Optimization.
8. Mesh Adaptation.
9. Meshing and Parallelism.
10. Applications.
11. Some Algorithms and Formulas.

About the authors


Paul Louis George is Director of Research at the French Institute for Research in Computer Science and Automation (Inria) and one of the most internationally recognized experts in meshing.

Houman Borouchaki is Professor at the University of Technology of Troyes (UTT) in France. He is an expert on meshing problems, geometric modeling and applications in solid mechanics.

Frédéric Alauzet and Adrien Loseille are researchers at Inria, both with particular expertise in meshing adaptation, error estimators, resolution methods (advanced solvers in fluid mechanics) and remeshing methods.

Patrick Laug is a researcher at Inria with particular expertise in geometric modeling and the generation of curve and surface meshes.

Loïc Maréchal, a long-time collaborator at Inria as an engineer, is an essential reference on hexahedra.