Highlights the Progression of Meshing Technologies and Their Applications
Finite Element Mesh Generationprovides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization.
It sets out the fundamentals of popular techniques, including:
- Delaunay triangulation
- Advancing-front (ADF) approach
- Quadtree/Octree techniques
- Refinement and optimization-based strategies
From the geometrical and the topological aspects and their associated operations and inter-relationships, each approach is vividly described and illustrated with examples. Beyond the algorithms, the book also explores the practice of using metric tensor and surface curvatures for generating anisotropic meshes on parametric space. It presents results from research including 3D anisotropic meshing, mesh generation over unbounded domains, meshing by means of intersection, re-meshing by Delaunay-ADF approach, mesh refinement and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods. The author provides illustrations of major meshing algorithms, pseudo codes, and programming codes in C++ or FORTRAN.
Geared toward research centers, universities, and engineering companies, Finite Element Mesh Generation describes mesh generation methods and fundamental techniques, and also serves as a valuable reference for laymen and experts alike.
Table of Contents
Finite element method
What is finite element mesh generation?
Why finite element mesh generation?
Problem definition, scope and philosophy, science or art?
General strategies, robustness, difficulties and methodologies
So far achieved and what lies ahead
Topics discussed in the chapters
Notations, symbols and abbreviations
Terminologies and data structures
Geometrical operations and formulas
Topological operations and algorithms
Mesh generation on planar domain
Structured mesh on planar domain
Unstructured mesh on planar domain
Meshing by quadtree decomposition
Delaunay triangulation (DT)
Advancing front approach
Meshing by a combined scheme of DT and ADF approach
Enhanced quadtree meshing
Mesh generation over curved surfaces
Parametric mapping method
Mesh generation by packing ellipses
Direct mesh generation on surface
Mesh generation by surface intersection
Quadrilateral surface mesh
Mesh generation in three dimensions
Delaunay triangulation (3D)
Boundary recovery for 3D DT
Boundary protection in DT
Generation of tetrahedral mesh by ADF approach
Generation of tetrahedral mesh by sphere packing
Generation of hexahedral mesh
Shape measure and quality coefficient
Optimisation by shifting of nodes
Optimisation by topological operations
Mesh generation by parallel processing
Fundamentals and strategies
Parallel Delaunay triangulation in 2D
Parallel Delaunay triangulation in 3D
Partition of discretised surface for parallel processing
Auxiliary meshing techniques
Surface verification and preparation
Multi-grid insertion of non-uniform point distributions (2D)
Multi-grid insertion of non-uniform point distributions (3D)
Mesh generation and adaptation by edge refinement
Meshing volume bounded by analytical curved surfaces
Merging of tetrahedral meshes
Merging of hexahedral meshes
Curvilinear finite element mesh
Adaptive refinement analysis
Daniel S.H. Lo received his Doc-Ing from L’Ecole Nationale des Ponts et Chaussees in France. He is currently a professor at the Department of Civil Engineering of the University of Hong Kong, and has been working on mesh generation for more than 30 years. Apart from numerous journal papers on mesh generation and finite element technology, Lo has also been the guest editor for two special issues on finite element mesh adaptation, co-author of a book on the finite element method, and author of book chapters on mesh generation.
"… the present monograph fills a gaping hole in the literature on scientific computing… it could be subtitled by 'All you want to know about mesh generation'."
—Zentralblatt MATH, 2015
"This book provides a well-structured and thorough treatment of very recent research on mesh generation, in a single well organized document. The descriptions of methods and algorithms are complete and provide readers with all the necessary information needed to implement on their own the algorithms and methods discussed in the book. Numerical examples provide concrete measures of the performance of the algorithms and can serve as a reference for those interested in validating their own implementations."
—Francois Guibault, Polytechnique Montreal, Canada
"…there are very few books on this subject. Daniel Lo’s book (examining the contents) offers a practical point of view and gives details on some topics which, I think, are not cover[ed] by the other books on meshing techniques."
—Houman Borouchaki, Université de Technologie de Troyes, France
"This book brings together the major propulsion system components with control oriented models and actuators to enable software and hardware-in-the-loop simulations. … This book will provide students with a detailed set of component models and simulation tools to learn Rapid Control Prototyping methods."
—Douglas J. Nelson, Professor of Mechanical Engineering, Virginia Tech
"This book is aimed at those who want a comprehensive overview of the techniques of finite-element mesh generation. The techniques and algorithms are clearly explained and there are good references to follow up where greater detail is required. However, there is probably a broader readership among practising engineers, who use the finite-element method on a daily basis, and who want a better understanding of the tools they rely on as a basis for their calculations."
—Stephen Hendry, Engineering and Computational Mechanics