Meshless Methods And Their Numerical Properties

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Meshless Methods And Their Numerical Properties

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Author : Hua Li
language : en
Publisher: CRC Press
Release Date : 2013-02-22

Meshless Methods And Their Numerical Properties written by Hua Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-22 with Mathematics categories.

A comprehensive introduction to meshless methods, this book gives complete mathematical formulations for the most important and classical methods, as well as several recently developed by the authors. It also offers a rigorous mathematical treatment of their numerical properties-including consistency, convergence, stability, and adaptivity-to help you choose the method that is best for your needs. The book contains several examples of engineering applications, including the nonlinear fluid-structure analysis of near-bed submarine pipelines and the two-dimensional multiphysics simulation of pH-sensitive hydrogels.

Meshless Methods And Their Numerical Properties

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Author : Hua Li
language : en
Publisher: CRC Press
Release Date : 2017-03-29

Meshless Methods And Their Numerical Properties written by Hua Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-29 with categories.

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical properties�including consistency, convergence, stability, and adaptivity�to help you choose the method that is best suited for your needs. Get Guidance for Developing and Testing Meshless Methods Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods. Explore Engineering Applications of Meshless Methods The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods. Choose the Best Method for a Particular Problem Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.

An Introduction To Meshfree Methods And Their Programming

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Author : G.R. Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05

An Introduction To Meshfree Methods And Their Programming written by G.R. Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Technology & Engineering categories.

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

Mesh Free Methods

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Author : G.R. Liu
language : en
Publisher: CRC Press
Release Date : 2002-07-29

Mesh Free Methods written by G.R. Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-29 with Mathematics categories.

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,

Meshfree Methods

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Author : G.R. Liu
language : en
Publisher: CRC Press
Release Date : 2009-10-06

Meshfree Methods written by G.R. Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-06 with Mathematics categories.

Understand How to Use and Develop Meshfree TechniquesAn Update of a Groundbreaking WorkReflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edit

Frontiers Of Numerical Analysis

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Author : James Blowey
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Frontiers Of Numerical Analysis written by James Blowey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Computers categories.

Contains lecture notes on four topics at the forefront of research in computational mathematics. This book presents a self-contained guide to a research area, an extensive bibliography, and proofs of the key results. It is suitable for professional mathematicians who require an accurate account of research in areas parallel to their own.

Biodental Engineering Iv

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Author : R.M. Natal Jorge
language : en
Publisher: CRC Press
Release Date : 2017-11-14

Biodental Engineering Iv written by R.M. Natal Jorge and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-14 with Medical categories.

Since dentistry is a branch of medicine with its own peculiarities and very diverse areas of action, it can be considered as an interdisciplinary field. BIODENTAL ENGINEERING IV contains the full papers presented at the 4th International Conference on Biodental Engineering (BIODENTAL 2016, Vila Nova de Famalicão, Portugal, 21—23 June 2016), and covers the use of new techniques and technologies in dentistry. The contributions provide a comprehensive coverage of the state-of-the art in this area, and addresses the following topics: • Aesthetics • Bioengineering • Biomaterials • Biomechanical disorders • Biomedical devices • Computational bio- imaging and visualization • Computational methods • Dental medicine • Experimental mechanics • Signal processing and analysis • Implantology • Minimally invasive devices and techniques • Orthodontics • Prosthesis and orthosis • Simulation • Software development • Telemedicine • Tissue engineering • Virtual reality BIODENTAL ENGINEERING IV will be of interest to academics and professionals involved or interested in dentistry, biomechanical disorders, numerical simulation, orthodontics, implantology, aesthetics, dental medicine, medical devices and medical imaging.

Reduced Modelling Of Planar Fuel Cells

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Author : Zhongjie He
language : en
Publisher: Springer
Release Date : 2016-12-25

Reduced Modelling Of Planar Fuel Cells written by Zhongjie He and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-25 with Technology & Engineering categories.

This book focuses on novel reduced cell and stack models for proton exchange membrane fuel cells (PEMFCs) and planar solid oxide fuel cells (P-SOFCs) that serve to reduce the computational cost by two orders of magnitude or more with desired numerical accuracy, while capturing both the average properties and the variability of the dependent variables in the 3D counterparts. The information provided can also be applied to other kinds of plate-type fuel cells whose flow fields consist of parallel plain channels separated by solid ribs. These fast and efficient models allow statistical sensitivity analysis for a sample size in the order of 1000 without prohibitive computational cost to be performed to investigate not only the individual, but also the simultaneous effects of a group of varying geometrical, material, and operational parameters. This provides important information for cell/stack design, and to illustrate this, Monte Carlo simulation of the reduced P-SOFC model is conducted at both the single-cell and stack levels.

Meshfree Methods For Partial Differential Equations Viii

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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2017-04-05

Meshfree Methods For Partial Differential Equations Viii written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Computers categories.

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

Meshless Methods In Biomechanics

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Author : Jorge Belinha
language : en
Publisher: Springer
Release Date : 2014-05-14

Meshless Methods In Biomechanics written by Jorge Belinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Technology & Engineering categories.

This book presents the complete formulation of a new advanced discretization meshless technique: the Natural Neighbour Radial Point Interpolation Method (NNRPIM). In addition, two of the most popular meshless methods, the EFGM and the RPIM, are fully presented. Being a truly meshless method, the major advantages of the NNRPIM over the FEM and other meshless methods, are the remeshing flexibility and the higher accuracy of the obtained variable field. Using the natural neighbour concept, the NNRPIM permits to determine organically the influence-domain, resembling the cellulae natural behaviour. This innovation permits the analysis of convex boundaries and extremely irregular meshes, which is an advantage in the biomechanical analysis, with no extra computational effort associated. This volume shows how to extend the NNRPIM to the bone tissue remodelling analysis, expecting to contribute with new numerical tools and strategies in order to permit a more efficient numerical biomechanical analysis.