Some Advantages of the Elliptic Weight Function for the Element Free Galerkin Method

2005 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mohsen Asghari
Keyword(s):  
Weight Function ◽  
Galerkin Method ◽  
Computational Cost ◽  
Characteristic Parameter ◽  
Major Influence ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Influence Radius ◽  
Anisotropic Weight ◽  
Element Free

In this paper, an anisotropic weight function in the elliptic form is introduced for the Element Free Galerkin Method (EFGM). In the circular (isotropic) weight function, each node has one characteristic parameter that determines its domain of influence. In the elliptic weight function, each node has three characteristic parameters that are major influence radius, minor influence radius and the direction of the major influence. Using the elliptic weight function each point of the domain may be affected by a less number of nodes in certain conditions. Thus, the computational cost of the method is decreased. In addition, the dependency of the solution on the method that is used for the enforcement of the essential boundary conditions, decreases. As an application of the proposed elliptic weight function, some examples of elastostatic problems are solved and the results are compared with those available in the literature.

Influence of selectable parameters in element-free Galerkin method: One-dimensional bar axially loaded problem

2008 ◽  
Vol 222 (9) ◽  
pp. 1621-1633 ◽  
Author(s):  
O F Valencia ◽  
F J Gómez-Escalonilla ◽  
J López Díez
Keyword(s):  
Galerkin Method ◽  
Computational Cost ◽  
Axial Loads ◽  
Element Free Galerkin Method ◽  
One Dimensional ◽  
Practical Applications ◽  
Element Free Galerkin ◽  
Support Size ◽  
Optimal Values ◽  
Element Free

Meshless methods (MMs) have become interesting and promising methods in solving partial differential equations, because of their flexibility in practical applications when compared with the standard finite-element method (e.g. crack propagation, large deformations, and so on). Implementation of these methods requires a good understanding of the influence of some specific selectable parameters. In this article, those parameters are analysed for one of the most popular MMs, the element-free Galerkin method, considering both accuracy and computational cost. Thus, the dependence of the solutions on grid irregularity, order of the polynomial basis, type of weight function, and the support size is investigated, and conclusions are drawn with respect to recommended or ‘optimal’ values for one-dimensional bar problems with applied axial loads.

scholarly journals Element-Free Galerkin Method Based on Block-Pulse Wavelets Integration for Solving Fourth-Order Obstacle Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Azam ◽  
Khalid Parvez ◽  
Muhammad Omair
Keyword(s):  
Galerkin Method ◽  
Fourth Order ◽  
Computational Cost ◽  
Contact Problems ◽  
Weight Functions ◽  
Test Problems ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Technique Comparison

We introduce improved element-free Galerkin method based on block pulse wavelet integration for numerical approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. Moving least squares (MLS) approach is used to construct shape functions with optimized weight functions and basis. Numerical results for test problems are presented in this article to elaborate the pertinent features for the proposed technique. Comparison with existing techniques shows that our proposed method based on integration technique provides better approximation at reduced computational cost.

Bending Solution of Plates on Winkler Foundation by Element-Free Galerkin Method Based on Mindlin Plate Theory

2012 ◽  
Vol 166-169 ◽  
pp. 3136-3141
Author(s):  
Min Yan Xu ◽  
Jian Dong Sun ◽  
Shi Qi Cui ◽  
Lei Shi
Keyword(s):  
Weight Function ◽  
Galerkin Method ◽  
Plate Theory ◽  
Positive Definite Matrix ◽  
Mindlin Plate ◽  
Winkler Foundation ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Control Equation ◽  
Element Free

Element-free Galerkin method (EFGM) is successfully applied to solve the bending problem of plates on a Winkler foundation. The shape function which is characteristic of high-time continuity is formulated by means of weight function. A way to incorpor- ate the self-adaptive influential radius in weight function is proposed. Based on variational principle, this paper derives control equation for the bending of plates on a Winkler foundation from Mindlin-Reissner plate theory. Using penalty function mothed, assembled stiffness matrix which is real symmetry positive definite matrix is deduced. This method can solve the bending problem of plates with different boundary conditions on a Winkler foundation. The corresponding computer programs of EFGM and post-process programs are also developed. Numerical examples show that EFGM solving the bending of plates on a Winkler found is reasonable and feasible. This present study provides a newly effective numerical method for the Winkler foundation bending problem and expands the application field of EFGM.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

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