Finite Element Mesh Generation

Highlights the Progression of Meshing Technologies and Their Applications Finite Element Mesh Generation provides 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and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods.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.

Introduction 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 Mathematics Historical development So far achieved and what lies ahead Topics discussed in the chapters Fundamentals Introduction Notations, symbols and abbreviations Terminologies and data structures Geometrical operations and formulas Topological operations and algorithms Sorting Background grid Mesh generation on planar domain Introduction 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 Quadrilateral mesh Mesh generation over curved surfaces Introduction 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 Introduction Delaunay triangulation (3D) Boundary recovery for 3D DT Boundary protection in DT Generation of tetrahedral mesh by ADF approach Delaunay–ADF meshing Generation of tetrahedral mesh by sphere packing Generation of hexahedral mesh Mesh optimisation Introduction Shape measure and quality coefficient Optimisation by shifting of nodes Optimisation by topological operations Mesh generation by parallel processing Introduction 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 References Appendix Index

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.