Geometry And Topology For Mesh Generation

Author : Herbert Edelsbrunner
Publisher : Cambridge University Press
ISBN 13 : 9780521793094
Total Pages : 206 pages
Book Rating : 4.92/5 ( download)

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Download or read book Geometry and Topology for Mesh Generation written by Herbert Edelsbrunner and published by Cambridge University Press. This book was released on 2001-05-28 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.

Author : Siu-Wing Cheng
Publisher : CRC Press
ISBN 13 : 1584887311
Total Pages : 404 pages
Book Rating : 4.17/5 ( download)

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Download or read book Delaunay Mesh Generation written by Siu-Wing Cheng and published by CRC Press. This book was released on 2016-04-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Rubén Sevilla
Publisher : Springer Nature
ISBN 13 : 3030925404
Total Pages : 328 pages
Book Rating : 4.06/5 ( download)

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Download or read book Mesh Generation and Adaptation written by Rubén Sevilla and published by Springer Nature. This book was released on 2022-05-18 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.

Author : Yongjie Jessica Zhang
Publisher : CRC Press
ISBN 13 : 1315362562
Total Pages : 354 pages
Book Rating : 4.64/5 ( download)

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Download or read book Geometric Modeling and Mesh Generation from Scanned Images written by Yongjie Jessica Zhang and published by CRC Press. This book was released on 2018-09-03 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Yongjie (Jessica) Zhang
Publisher : Springer Science & Business Media
ISBN 13 : 940074255X
Total Pages : 302 pages
Book Rating : 4.50/5 ( download)

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Download or read book Image-Based Geometric Modeling and Mesh Generation written by Yongjie (Jessica) Zhang and published by Springer Science & Business Media. This book was released on 2012-07-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Herbert Edelsbrunner
Publisher : American Mathematical Society
ISBN 13 : 1470467690
Total Pages : 241 pages
Book Rating : 4.92/5 ( download)

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Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Society. This book was released on 2022-01-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Author : Daniel S.H. Lo
Publisher : CRC Press
ISBN 13 : 041569048X
Total Pages : 676 pages
Book Rating : 4.85/5 ( download)

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Download or read book Finite Element Mesh Generation written by Daniel S.H. Lo and published by CRC Press. This book was released on 2015-01-15 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean-Luc Mari
Publisher : John Wiley & Sons
ISBN 13 : 1786300419
Total Pages : 194 pages
Book Rating : 4.16/5 ( download)

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Download or read book Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis written by Jean-Luc Mari and published by John Wiley & Sons. This book was released on 2020-01-02 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.

Author : Joe F. Thompson
Publisher : CRC Press
ISBN 13 : 9781420050349
Total Pages : 1136 pages
Book Rating : 4.46/5 ( download)

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Download or read book Handbook of Grid Generation written by Joe F. Thompson and published by CRC Press. This book was released on 1998-12-29 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material. This handbook covers: Fundamental concepts and approaches Grid generation process Essential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfaces Cells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinations Separate grids overlaid on one another, communicating data through interpolation Moving boundaries and internal interfaces in the field Resolving gradients and controlling solution error Grid generation codes, both commercial and freeware, as well as representative and illustrative grid configurations Handbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners.

Author : Tamal Krishna Dey
Publisher : Cambridge University Press
ISBN 13 : 1009103199
Total Pages : 456 pages
Book Rating : 4.90/5 ( download)

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Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.