Meshfree Methods
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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 For Partial Differential Equations
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-18
Meshfree Methods For Partial Differential Equations written by Michael Griebel 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 2002-09-18 with Mathematics categories.
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.
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
Meshfree Particle Methods
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Author : Shaofan Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-07
Meshfree Particle Methods written by Shaofan Li 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 2007-03-07 with Mathematics categories.
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.
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.
Simulation Of Additive Manufacturing Using Meshfree Methods
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Author : Christian Weißenfels
language : en
Publisher: Springer Nature
Release Date : 2021-10-29
Simulation Of Additive Manufacturing Using Meshfree Methods written by Christian Weißenfels and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-29 with Technology & Engineering categories.
This book provides a detailed instruction to virtually reproduce the processes of Additive Manufacturing on a computer. First, all mathematical equations needed to model these processes are presented. Due to their flexibility, meshfree methods represent optimal computational solution schemes to simulate Additive Manufacturing processes. On the other hand, these methods usually do not guarantee an accurate solution. For this reason, this monograph is dedicated in detail to the necessary criteria for computational solution schemes to provide accurate results. Several meshfree methods are examined with respect to these conditions. Two different 3D printing techniques are presented in detail. The results obtained from the simulation are investigated and compared with experimental data. This work is addressed to both scientists and professionals working in the field of development who are interested to learn the secrets behind meshfree methods or get into the modeling of Additive Manufacturing.
Meshfree Methods For Partial Differential Equations
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Meshfree Methods For Partial Differential Equations written by Michael Griebel 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 2012-12-06 with Mathematics categories.
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.
Meshfree Methods For Partial Differential Equations Ii
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-21
Meshfree Methods For Partial Differential Equations Ii written by Michael Griebel 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 2006-09-21 with Mathematics categories.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.
Meshfree Approximation Methods With Matlab With Cd Rom
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Author : Gregory E Fasshauer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-04-17
Meshfree Approximation Methods With Matlab With Cd Rom written by Gregory E Fasshauer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-17 with Mathematics categories.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods.The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.