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and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods.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.

&Quot;This book describes both structured and unstructured mesh generation techniques. Structured mesh generation is covered briefly and the algebraic, multi-block technique is discussed in more detail. The main part of the book covers unstructured mesh generation using the advancing front, paving and Delaunay techniques. The Delaunay method is described in two and three dimensions. Both theoretical and implementation issues are discussed in detail. An integrated framework that is used for the two dimensional unstructured methods is also described. Common features of the framework include: accurate control over mesh size; boundary refinement procedures; and postprocessing tasks such as smoothing. Methods to convert triangular meshes to quadrilateral meshes are also presented. Mesh quality of the different mesh generation procedures is addressed with some examples.". "The book will be of interest to engineers, computer scientists and mathematicians working on mesh generation and finite element methods. The C source code for the procedures described in the book is available via the authors's website."--BOOK JACKET.

Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why thes

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.

This textbook demonstrates the application of the finite element philosophy to the solution of real-world problems and is aimed at graduate level students, but is also suitable for advanced undergraduate students. An essential part of an engineer’s training is the development of the skills necessary to analyse and predict the behaviour of engineering systems under a wide range of potentially complex loading conditions. Only a small proportion of real-life problems can be solved analytically, and consequently, there arises the need to be able to use numerical methods capable of simulating real phenomena accurately. The finite element (FE) method is one such widely used numerical method. Finite Element Applications begins with demystifying the ‘black box’ of finite element solvers and progresses to addressing the different pillars that make up a robust finite element solution framework. These pillars include: domain creation, mesh generation and element formulations, boundary conditions, and material response considerations. Readers of this book will be equipped with the ability to develop models of real-world problems using industry-standard finite element packages.

Cutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing, geometric modeling, and mesh generation with the finite element method (FEM) to solve problems in computational biology, medicine, materials science, and engineering. Based on the author’s recent research and course at Carnegie Mellon University, the text explains the fundamentals of medical imaging, image processing, computational geometry, mesh generation, visualization, and finite element analysis. It also explores novel and advanced applications in computational biology, medicine, materials science, and other engineering areas. One of the first to cover this emerging interdisciplinary field, the book addresses biomedical/material imaging, image processing, geometric modeling and visualization, FEM, and biomedical and engineering applications. It introduces image-mesh-simulation pipelines, reviews numerical methods used in various modules of the pipelines, and discusses several scanning techniques, including ones to probe polycrystalline materials. The book next presents the fundamentals of geometric modeling and computer graphics, geometric objects and transformations, and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.

As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion, quality improvement, mesh warping, heterogeneous materials, biomodelcular modeling and simulation, as well as medical and engineering applications. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion, quality improvement, mesh warping, heterogeneous materials, biomodelcular modeling and simulation, as well as medical and engineering applications. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion, quality improvement, mesh warping, heterogeneous materials, biomodelcular modeling and simulation, as well as medical and engineering applications. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion, quality improvement, mesh warping, heterogeneous materials, biomodelcular modeling and simulation, as well as medical and engineering applications.