An Introduction to Meshfree Methods and Their Programming

An Introduction to Meshfree Methods and Their Programming
Author: G.R. Liu
Publisher: Springer Science & Business Media
Total Pages: 497
Release: 2005-12-05
Genre: Technology & Engineering
ISBN: 1402034687


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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.


An Introduction to Meshfree Methods and Their Programming
Language: en
Pages: 497
Authors: G.R. Liu
Categories: Technology & Engineering
Type: BOOK - Published: 2005-12-05 - Publisher: Springer Science & Business Media

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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
Meshless Methods and Their Numerical Properties
Language: en
Pages: 429
Authors: Hua Li
Categories: Mathematics
Type: BOOK - Published: 2013-02-22 - Publisher: CRC Press

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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
Meshfree and Particle Methods
Language: en
Pages: 509
Authors: Ted Belytschko
Categories: Mathematics
Type: BOOK - Published: 2023-12-13 - Publisher: John Wiley & Sons

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Meshfree and Particle Methods Provides thorough coverage of essential concepts and state-of-the-art developments in the field Meshfree and Particle Methods is t
Meshfree Approximation Methods with MATLAB
Language: en
Pages: 520
Authors: Gregory E. Fasshauer
Categories: Technology & Engineering
Type: BOOK - Published: 2007 - Publisher: World Scientific

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Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of mes
Mesh Free Methods
Language: en
Pages: 715
Authors: G.R. Liu
Categories: Mathematics
Type: BOOK - Published: 2002-07-29 - Publisher: CRC Press

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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 u