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.

scholarly journals Characterizing Flexoelectricity in Composite Material Using the Element-Free Galerkin Method

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 271 ◽  
Author(s):  
Bo He ◽  
Brahmanandam Javvaji ◽  
Xiaoying Zhuang
Keyword(s):  
Composite Material ◽  
Galerkin Method ◽  
Strain Gradient ◽  
Electromechanical Coupling ◽  
Mechanical Energy ◽  
Weight Functions ◽  
Gradient Term ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

This study employs the Element-Free Galerkin method (EFG) to characterize flexoelectricity in a composite material. The presence of the strain gradient term in the Partial Differential Equations (PDEs) requires C 1 continuity to describe the electromechanical coupling. The use of quartic weight functions in the developed model fulfills this prerequisite. We report the generation of electric polarization in a non-piezoelectric composite material through the inclusion-induced strain gradient field. The level set technique associated with the model supervises the weak discontinuity between the inclusion and matrix. The increased area ratio between the inclusion and matrix is found to improve the conversion of mechanical energy to electrical energy. The electromechanical coupling is enhanced when using softer materials for the embedding inclusions.

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.

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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