On boundary conditions in the element-free Galerkin method

1997 ◽  
Vol 19 (4) ◽  
pp. 264-270 ◽  
Author(s):  
Y. X. Mukherjee ◽  
S. Mukherjee
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

FURTHER INVESTIGATION OF ELEMENT-FREE GALERKIN METHOD USING MOVING KRIGING INTERPOLATION

2004 ◽  
Vol 01 (02) ◽  
pp. 345-365 ◽  
Author(s):  
P. TONGSUK ◽  
W. KANOK-NUKULCHAI
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Least Square ◽  
Kriging Interpolation ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
Basic Premise ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

Following its first introduction, this study further scrutinizes the new type of shape functions for Element-free Galerkin Method (EFGM) based on the Moving Kriging (MK) interpolation. Kriging is a geostatistical method of spatial interpolation. Its basic premise is that every unknown point can be interpolated from known scattered points in its specified neighborhood. This property is ideal for EFGM. Previously, a shortcoming of EFGM based on Moving Least Square (MLS) approximation is associated with its limitation to satisfy essential boundary conditions exactly. With MK interpolation functions, EFGM solution can satisfy essential boundary conditions automatically. Numerical tests on one and two-dimensional elasticity problems have confirmed the effectiveness of MK in addressing this specific shortcoming of EFGM. Furthermore, the study also finds the accuracy of EFGM to be greatly enhanced with the use of MK shape functions.

scholarly journals Bernstein polynomials in element-free Galerkin method

2011 ◽  
Vol 225 (8) ◽  
pp. 1808-1815 ◽  
Author(s):  
O F Valencia ◽  
F J Gómez-Escalonilla ◽  
D Garijo ◽  
J L Díez
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Bernstein Polynomials ◽  
Partition Of Unity ◽  
Particle Method ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves, can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

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