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An Introduction to Meshfree Methods and Their Programming

  • Book
  • © 2005

Overview

Authors:
  1. G.R. Liu

    1. National University of Singapore, Singapore

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    You can also search for this author in PubMed   Google Scholar

  2. Y.T. Gu

    1. National University of Singapore, Singapore

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Friendly and straightforward presentation and beginner orientated
  • Provides the fundamentals of numerical analysis that are particularly important to meshfree methods.
  • Wide coverage of meshfree methods: EFG, RPIM, MLPG, LRPIM, MWS and collocation methods
  • Detailed comparison case studies for many existing meshfree methods
  • Well-tested computer source codes are attached with useful descriptions and readily test examples
  • Soft copy of these source codes are available also at http://www.nus.edu.sg/ACES

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xx
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  2. Fundamentals

    Pages 1-36

  3. Overview of Meshfree Methods

    Pages 37-53

  4. Meshfree Shape Function Construction

    Pages 54-144

  5. Meshfree Methods Based on Global Weak-Forms

    Pages 145-236

  6. Meshfree Methods Based on Local Weak-Forms

    Pages 237-309

  7. Meshfree Collocation Methods

    Pages 310-379

  8. Meshfree Methods Based on Combination of Local Weak-Form and Collocation

    Pages 380-453

  9. Back Matter

    Pages 454-479
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Keywords

About this book

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.

Authors and Affiliations

  • National University of Singapore, Singapore

    G.R. Liu, Y.T. Gu

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