The element-free Galerkin method based on moving least squares and moving Kriging approximations for solving two-dimensional tumor-induced angiogenesis model

2019 ◽  
Vol 36 (4) ◽  
pp. 1517-1537 ◽  
Author(s):  
Mehdi Dehghan ◽  
Niusha Narimani
Keyword(s):  
Galerkin Method ◽  
Least Squares ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Angiogenesis Model

A NEW ELEMENT-FREE GALERKIN METHOD BASED ON IMPROVED COMPLEX VARIABLE MOVING LEAST-SQUARES APPROXIMATION FOR ELASTICITY

2012 ◽  
Vol 01 (01) ◽  
pp. 1250011 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Complex Variable ◽  
Weak Form ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Elasticity Problems ◽  
Element Free

In this paper, by constructing a new functional, an improved complex variable moving least-squares (ICVMLS) approximation is presented. Based on element-free Galerkin (EFG) method and the ICVMLS approximation, a new complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented. Galerkin weak form is used to obtain the discretized equations and the essential boundary conditions are applied with Lagrange multiplier. Then the formulae of the new CVEFG method for two-dimensional elasticity problems are obtained. Compared with the conventional EFG method, the new CVEFG method has greater computational precision and efficiency. For the purposes of demonstration, some selected numerical examples are solved using the ICVEFG method.

The influence of selectable parameters in the element-free Galerkin method: A one-dimensional beam-in-bending problem

2009 ◽  
Vol 223 (7) ◽  
pp. 1579-1590 ◽  
Author(s):  
O F Valencia ◽  
F J Gómez-Escalonilla ◽  
J López-Díez
Keyword(s):  
Galerkin Method ◽  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
One Dimensional ◽  
Element Free Galerkin ◽  
Axially Loaded ◽  
Element Free

Continuing with the analysis performed for the one-dimensional axially loaded bar problem, a beam in bending is analysed to understand the influence of the characteristic parameters that have any influence in the solution of this problem using the element-free Galerkin method (EFGM), one of the most popular meshless methods. Both accuracy and time cost are considered as the evaluation functions to perform such an analysis. Both functions provide a reasonable idea to consider EFGM as an adequate method to solve the problem considered in this article. As in a one-dimensional axially loaded bar problem, the parameters to be considered will be those that affect the solution: number of nodes in which the domain is modelled, the nodes scatter, the order of the polynomial base to generate shape functions, the order of the quadrature to solve integrals, and the support radius. Besides, as in a one-dimensional axially loaded problem, some cases with different loading and stiffness conditions are considered. However, in this analysis a generalized moving least squares method is used to create shape functions instead of the moving least squares.

Sign in / Sign up

Export Citation Format

Share Document