This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

Modeling of heterogeneous materials and media is a problem of fundamental importance to
a wide class of phenomena and systems, ranging from condensed matter physics, soft …

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 …

Abstract Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical
approach which has attracted significant attention in the last two decades. Compared with …

Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has
broad prospects in modeling a wide range of problems in engineering and science …

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 …

In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …

A new continuous reproducing kernel interpolation function which explores the attractive
features of the flexible time-frequency and space-wave number localization of a window …

Meshless approximations based on moving least-squares, kernels, and partitions of unity
are examined. It is shown that the three methods are in most cases identical except for the …

A new finite element method is presented that features the ability to include in the finite
element space knowledge about the partial differential equation being solved. This new …