Based on the peridynamic (PD) theory introduced by Dr. Stewart A. Silling from Sandia
National Laboratories in 2000, this book presents the nonlocal PD differential operator and …

The concise review systematically summarises the state-of-the-art variants of Moving Least
Squares (MLS) method. MLS method is a mathematical tool which could render cogent …

The moving least square (MLS) approximation is one of the most important methods to
construct approximation functions in meshless methods. For the error analysis of the MLS …

Recently, because of simplicity of meshless methods, they have been employed for solving
many partial differential equations. One of the meshless methods is element free Galerkin …

The low cycle fatigue (LCF) life of aeroengine turbine blisk endures uncertain and transient
loads from multi-physical fields, so that it is necessary to evaluate the LCF life for improving …

This study presents the peridynamic approximation of a field variable and its temporal and
spatial derivatives based on least squares minimization. Such capability permits the …

It is notable that, the nonlocal reaction-diffusion equation carries math and computational
physics to the core of extremely dynamic multidisciplinary studies that emerge from a huge …

The complex variable element-free Galerkin (CVEFG) method is an efficient meshless
Galerkin method that uses the complex variable moving least squares (CVMLS) …

Increased attention has been paid on numerical modeling of interface problems as its wide
applications in various aspects of science. Motivated by enhancing the application of the …

In this paper, the basis functions are firstly constructed by employing the reproducing kernel
functions (RKFs). Based on these basis functions and an appropriate choice of the …