Meshless Methods and Their Numerical Properties

Author: Hua Li
Publisher: CRC Press
ISBN: 1466517468
Format: PDF
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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

Author: G.R. Liu
Publisher: Springer Science & Business Media
ISBN: 9781402034688
Format: PDF, ePub, Docs
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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.

Meshfree Methods

Author: G.R. Liu
Publisher: CRC Press
ISBN: 9781420082104
Format: PDF
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Understand How to Use and Develop Meshfree Techniques An Update of a Groundbreaking Work Reflecting 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 edition addresses important new developments, especially on essential theoretical issues. New to the Second Edition Much more details on fundamental concepts and important theories for numerical methods Discussions on special properties of meshfree methods, including stability, convergence, accurate, efficiency, and bound property More detailed discussion on error estimation and adaptive analysis using meshfree methods Developments on combined meshfree/finite element method (FEM) models Comparison studies using meshfree and FEM Drawing on the author’s own research, this book provides a single-source guide to meshfree techniques and theories that can effectively handle a variety of complex engineering problems. It analyzes how the methods work, explains how to use and develop the methods, and explores the problems associated with meshfree methods. To access MFree2D (copyright, G. R. Liu), which accompanies MESHFREE METHODS: MOVING BEYOND THE FINITE ELEMENT METHOD, Second Edition (978-1-4200-8209-8) by Dr. G. R. Liu, please go to the website: www.ase.uc.edu/~liugr An access code is needed to use program – to receive it please email Dr. Liu directly at: [email protected] Dr. Liu will reply to you directly with the code, and you can then proceed to use the software.

Progress on Meshless Methods

Author: A. J. M. Ferreira
Publisher: Springer Science & Business Media
ISBN: 1402088213
Format: PDF, Mobi
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In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Environmental Contaminants

Author: Tarun Gupta
Publisher: Springer
ISBN: 9811073325
Format: PDF, Mobi
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This book addresses the measurement of environmental contaminants in water, air, and soil. It also presents modifications of and improvements to existing control technologies for remediation of environmental contaminants. It covers improved designs of wastewater systems and innovations in designing newer membranes for water treatment. In addition, it includes two separate sections on the modelling and control of different existing and emerging pollutants. It covers major topics such as: pharmaceutical wastes, paper and pulp waste, poly aromatic hydrocarbons, mining dust, bioaerosols, endosulphan, biomass combustion, and landfill design aspects. It also features chapters on environmental exposure and modelling of aerosol deposition within human lungs. The content of this book will be of interest to researchers, professionals, and policymakers whose work involves environmental contaminants and related solutions.

Meshfree Methods for Partial Differential Equations III

Author: Michael Griebel
Publisher: Springer Science & Business Media
ISBN: 3540462228
Format: PDF, ePub
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Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes

Author: Miguel Cerrolaza
Publisher: Academic Press
ISBN: 0128117192
Format: PDF, Mobi
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Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. Provides non-conventional analysis methods for modeling Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) Includes contributions from several world renowned experts in their fields Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems

Meshfree Particle Methods

Author: Shaofan Li
Publisher: Springer Science & Business Media
ISBN: 3540222561
Format: PDF, ePub
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Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors ́ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state of the art on Meshfree Particle Methods.

Reduced Modelling of Planar Fuel Cells

Author: Zhongjie He
Publisher: Springer
ISBN: 331942646X
Format: PDF
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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

Author: Michael Griebel
Publisher: Springer Science & Business Media
ISBN: 3642561039
Format: PDF, ePub
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Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.