Eighty years of the finite element method: Birth, evolution, and future

WK Liu, S Li, HS Park - Archives of Computational Methods in …, 2022 - Springer
This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

Meshless methods: a review and computer implementation aspects

VP Nguyen, T Rabczuk, S Bordas, M Duflot - Mathematics and computers …, 2008 - Elsevier
The aim of this manuscript is to give a practical overview of meshless methods (for solid
mechanics) based on global weak forms through a simple and well-structured MATLAB …

[BOOK][B] Smoothed particle hydrodynamics: a meshfree particle method

GR Liu, MB Liu - 2003 - books.google.com
Page 1 Smoothed Particle Hydrodynamics a meshfree particle method GR Liu ↑ MB Liu Page
2 Page 3 1 Smoothed Particle Hydrodynamics a meshfree particle method This One …

A new class of accurate, mesh-free hydrodynamic simulation methods

PF Hopkins - Monthly Notices of the Royal Astronomical Society, 2015 - academic.oup.com
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison
with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) …

[BOOK][B] Meshfree methods: moving beyond the finite element method

GR Liu - 2009 - taylorfrancis.com
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 …

[BOOK][B] An introduction to meshfree methods and their programming

GR Liu, YT Gu - 2005 - books.google.com
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 …

A stabilized conforming nodal integration for Galerkin mesh‐free methods

JS Chen, CT Wu, S Yoon, Y You - International journal for …, 2001 - Wiley Online Library
Abstract Domain integration by Gauss quadrature in the Galerkin mesh‐free methods adds
considerable complexity to solution procedures. Direct nodal integration, on the other hand …

A point interpolation meshless method based on radial basis functions

JG Wang, GR Liu - International Journal for Numerical Methods …, 2002 - Wiley Online Library
A point interpolation meshless method is proposed based on combining radial and
polynomial basis functions. Involvement of radial basis functions overcomes possible …

Meshfree methods: progress made after 20 years

JS Chen, M Hillman, SW Chi - Journal of Engineering Mechanics, 2017 - ascelibrary.org
In the past two decades, meshfree methods have emerged into a new class of computational
methods with considerable success. In addition, a significant amount of progress has been …

Meshfree and particle methods and their applications

S Li, WK Liu - Appl. Mech. Rev., 2002 - asmedigitalcollection.asme.org
Recent developments of meshfree and particle methods and their applications in applied
mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed …