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Author: Klaus Hollig
Publisher: SIAM
ISBN: 9780898717532
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples.
Author: Klaus Hollig
Publisher: SIAM
ISBN: 9780898717532
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples.
Author: Klaus Hollig
Publisher: SIAM
ISBN: 0898716993
Category : Mathematics
Languages : en
Pages : 152
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Book Description
An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Author: Arkadiusz Żak
Publisher: Springer Nature
ISBN: 3031568362
Category :
Languages : en
Pages : 332
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Book Description
Author: Klaus Hollig
Publisher: SIAM
ISBN: 1611972949
Category : Mathematics
Languages : en
Pages : 228
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Book Description
B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Author: Jean-Daniel Boissonnat
Publisher: Springer Science & Business Media
ISBN: 3642274129
Category : Computers
Languages : en
Pages : 758
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Book Description
This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.
Author: E. Y. K. Ng
Publisher: CRC Press
ISBN: 1439869936
Category : Technology & Engineering
Languages : en
Pages : 432
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Book Description
Advanced image processing and mathematical modeling techniques are increasingly being used for the early diagnosis of eye diseases. A comprehensive review of the field, Human Eye Imaging and Modeling details the latest advances and analytical techniques in ocular imaging and modeling. The first part of the book looks at imaging of the fundus as well as infrared imaging. It begins by exploring developments in the analysis of fundus images, particularly for the diagnosis of diabetic retinopathy and glaucoma. It also reviews anterior segment imaging and reports on developments in ocular thermography, especially the use of thermal imaging as the basis of tear evaporimetry and dry eye diagnosis. The second part of the book delves into mathematical modeling of the human eye. Coverage includes modeling of the eye during retinal laser surgery, a framework for optical simulation, heat distribution using a 3D web-splines solution, and exposure to laser radiation. The text also examines computer simulation of the human eye based on principles of heat transfer, as well as various bioheat equations to predict interior temperatures based on the surface temperature. Featuring contributions by established experts in eye imaging, this is a valuable reference for medical personnel and researchers who want to know more about state-of-the-art computer-based imaging and detection methods. It presents novel imaging and modeling algorithms that can aid in early diagnosis, with the aim of enriching the lives of people suffering from eye abnormalities.
Author: Weihong Zhang
Publisher: Elsevier
ISBN: 0128213310
Category : Technology & Engineering
Languages : en
Pages : 352
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Book Description
The Feature-Driven Method for Structural Optimization details a novel structural optimization method within a CAD framework, integrating structural optimization and feature-based design. The book presents cutting-edge research on advanced structures and introduces the feature-driven structural optimization method by regarding engineering features as basic design primitives. Consequently, it presents a method that allows structural optimization and feature design to be done simultaneously so that feature attributes are preserved throughout the design process. The book illustrates and supports the effectiveness of the method described, showing potential applications through numerical modeling techniques and programming. This volume presents a high-performance optimization method adapted to engineering structures—a novel perspective that will help engineers in the computation, modeling and design of advanced structures. - Integrates two independent methods - structural optimization and feature-based design—into one framework - Adapts the high performance optimization method to the practice of designing engineering structures - Provides numerical evidence for the effectiveness and potential of the methods described - Works within a computer-aided design framework to develop a novel structural optimization methodology - Presents engineering features as the basic design primitives in structural optimization
Author: Timon Rabczuk
Publisher: Academic Press
ISBN: 0128141077
Category : Technology & Engineering
Languages : en
Pages : 640
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Book Description
Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. - Explains all the important theory behind XFEM and meshfree methods - Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes - Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods - Introduces alternative modeling methods to help readers decide what is most appropriate for their work
Author: Chongmin Song
Publisher: John Wiley & Sons
ISBN: 1119388457
Category : Science
Languages : en
Pages : 775
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Book Description
An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
Author: Wolfgang E. Nagel
Publisher: Springer Science & Business Media
ISBN: 3540747397
Category : Mathematics
Languages : en
Pages : 661
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Book Description
This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Stuttgart High Performance Computing Center in 2007. The reports cover all fields of computational science and engineering, with emphasis on industrially relevant applications. Presenting results for both vector-based and microprocessor-based systems, the book allows comparison between performance levels and usability of various architectures.
