Mesh Generation: Application to Finite Elements

✍ Scribed by Pascal Frey, Paul Louis George

• Publisher: Wiley-ISTE
• Year: 2008
• Tongue: English
• Leaves: 848
• Edition: 2
• Category: Library

✦ Synopsis

The aim of the second edition of this book is to provide a comprehensive survey of the different algorithms and data structures useful for triangulation and meshing construction. In addition, several aspects are given full coverage, such as mesh modification tools, mesh evaluation criteria, mesh optimization, adaptive mesh construction and parallel meshing techniques.
This new edition has been comprehensively updated and also includes a new chapter on mobile or deformable meshes.

✦ Table of Contents

Title page
Contents
Introduction
Symbols and Notations
1 General Definitions
1.1 Covering-up and triangulation
1.2 Mesh, mesh element, finite element mesh
1.3 Mesh data structures
1.4 Control space and neighborhood space
1.5 Mesh quality and mesh optimality
2 Basic Structures and Algorithms
2.1 Why use data structures?
2.2 Elementary structures
2.3 Basic notions about complexity
2.4 Sorting and searching
2.5 One-dimensional data structures
2.6 Two and three-dimensional data structures
2.7 Topological data structures
2.8 Robustness
2.9 Optimality of an implementation
2.10 Examples of generic algorithms
3 A Comprehensive Survey of Mesh Generation Methods
3.1 Classes of methods
3.2 Structured mesh generators
3.2.1 Algebraic interpolation methods
3.2.2 PDE-based methods
3.2.3 Multiblock method
3.2.4 Product method (topology-based method)
3.3 Unstructured mesh generators
3.3.1 Spatial decomposition methods
3.3.2 Advancing-front method
3.3.3 Delaunay technique
3.3.4 Tentative comparison of the three classical methods
3.3.5 Other methods
3.4 Surface meshing
3.4.1 Mesh generation via a parametric space
3.4.2 Implicit surface triangulation
3.4.3 Direct surface meshing
3.4.4 Surface remeshing
3.5 Mesh adaptation
3.6 Parallel unstructured meshing
4 Algebraic, PDE and Multiblock Methods
4.1 Algebraic methods
4.1.1 Trivial mapping functions
4.1.2 Quadrilateral or triangular analogy
4.1.3 Surface meshing
4.1.4 Hexahedral, pentahedral or tetrahedral analogy
4.1.5 Other algebraic methods and alternative methods
4.2 PDE-based methods
4.2.1 Basic ideas
4.2.2 Surface meshing and complex shapes
4.3 Multiblock method
4.3.1 Basic ideas
4.3.2 Partitioning the domain
4.3.3 Computational issues and application examples
5 Quadtree-octree Based Methods
5.1 Overview of spatial decomposition methods
5.2 Classical tree-based mesh generation
5.3 Governed tree-based method
5.4 Other approaches
5.5 Extensions
6 Advancing-front Technique for Mesh Generation
6.1 A classical advancing-front technique
6.2 Governed advancing-front method
6.3 Application examples
6.4 Combined approaches
6.5 Extensions
7 Delaunay-based Mesh Generation Methods
7.1 Vorono'i diagram and Delaunay triangulation
7.2 Constrained triangulation
7.2.1 Maintaining a constrained entity
7.2.2 Enforcing a constraint
7.3 Classical Delaunay meshing
7.3.1 Simplified Delaunay type triangulation method
7.3.2 Boundary integrity and domain identification
7.3.3 Field point creation
7.3.4 Optimization
7.3.5 Practical issues
7.3.6 Application examples
7.4 Other methods
7.4.1 Point insertion methods
7.4.2 Field point creation
7.4.3 Boundary enforcement
7.5 Isotropic governed Delaunay meshing
7.6 Extensions
7.6.1 Weighted Delaunay triangulation
7.6.2 Anisotropic Delaunay meshing
7.6.3 Surface meshing
8 Other Types of Mesh Generation Methods
8.1 Product method
8.2 Grid or pattern-based methods
8.3 Optimization-based method
8.4 Quads by means of triangle combination
8.5 Quads by means of a direct method
8.6 Hex meshing
8.7 Miscellaneous
9 Delaunay Admissibility, Medial Axis and Applications
9.1 Delaunay-admissible set of segments in R2
9.2 Delaunay-admissible set of segments in R3
9.3 Delaunay-admissible set of triangular faces
9.4 Medial axis
9.5 Mid-surface
9.6 Applications
10 Quadratic Forms and Metrics
10.1 Bilinear and quadratic forms
10.2 Distances and lengths
10.3 Metric-based operations
10.4 Metric construction
10.4.1 Parametric surface meshing
10.4.2 Finite element simulation with error control
11 Differential Geometry
11.1 Metric properties of curves and arcs
11.2 Metric properties of a surface
11.3 Computational issues about surfaces
11.4 Non-linear problems
12 Curve Modeling
12.1 Interpolation and smoothing techniques
12.2 Lagrange and Hermite interpolation
12.3 Explicit construction of a composite curve
12.4 Control polygon based methods
12.5 Bezier curves
12.6 Prom composite curves to B-splines
12.7 Rational curves
12.8 Curve definitions and numerical issues
12.9 Towards a pragmatic curve definition?
13 Surface Modeling
13.1 Specific surfaces
13.2 Interpolation-based surfaces
13.3 Tensor product and control polyhedron
13.4 Triangular patches and Bezier triangles
13.5 Other types of patches
13.6 Composite surfaces
13.7 Explicit construction of a composite surface
14 Curve Meshing
14.1 Meshing a segment
14.2 Meshing a parametric curve
14.3 Curve meshing using a discrete definition
14.4 Re-meshing algorithm
14.5 Curves in K3
15 Surface Meshing and Re-meshing
15.1 Curve meshing (curve member of a surface)
15.2 First steps in surface meshing
15.3 A single patch
15.4 Multi-patches surface (patch-dependent)
15.5 Multi-patches surface (patch-independent)
15.6 Ill-defined multi-patches surface
15.7 Molecular surfaces
15.8 Surface reconstruction
15.9 Discrete surface (re-meshing process)
16 Meshing Implicit Curves and Surfaces
16.1 Review of implicit functions
16.2 Implicit function and meshing
16.3 Implicit curve meshing
16.4 Implicit surface meshing
16.5 Extensions
17 Mesh Modifications
17.1 Mesh (geometric) modifications
17.2 Merging two meshes
17.3 Node creation and node labeling
17.4 Renumbering issues
17.5 Miscellaneous
18 Mesh Optimization
18.1 About element measurement
18.2 Mesh quality (classical case)
18.3 Mesh quality (isotropic and anisotropic case)
18.4 Tools for mesh optimization
18.5 Strategies for mesh optimization
18.6 Computational issues
18.7 Application examples
19 Surface Mesh Optimization
19.1 Quality measures
19.2 Discrete evaluation of surface properties
19.3 Constructing a geometric support
19.4 Optimization operators
19.5 Optimization methods
19.6 Application examples
20 A Touch of Finite Elements
20.1 Introduction to a finite element style computation
20.2 Definition and first examples of finite elements
20.3 Error estimation and convergence
20.4 Stiffness matrix and right-hand side
20.5 A few examples of popular finite elements
21 Mesh Adaptation and H-methods
21.1 Control space (background mesh)
21.2 Adaptation by local modifications
21.3 Global isotropic adaptation method
21.4 Global anisotropic adaptation method
21.5 Adaptation
21.5.1 General framework of a local adaptation method
21.5.2 General framework of a global adaptation method
21.6 Application examples
22 Mesh Adaptation and ? or ßð-methods
22.1 P2 mesh
22.2 P-compatibility
22.3 Construction of P2 elements
22.4 Elements of higher degree
22.5 P-methods and ??-methods
23 Moving or Deformable Meshing Techniques
23.1 Rigid body motion
23.2 ALE methods
23.3 Mesh deformation
23.4 Interface tracking
24 Parallel Computing and Meshing Issues
24.1 Partition of a domain
24.2 Parallel meshing process
24.3 Parallel meshing techniques
Bibliography
Index