Moving kriging interpolation and element-free Galerkin method

2002 ◽  
Vol 56 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Lei Gu
Keyword(s):  
Galerkin Method ◽  
Kriging Interpolation ◽  
Element Free Galerkin Method ◽  
Moving Kriging Interpolation ◽  
Element Free Galerkin ◽  
Element Free

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.

An Element-Free Galerkin Method Based on Complex Variable Moving Kriging Interpolation for Potential Problems

2016 ◽  
Vol 13 (03) ◽  
pp. 1650013
Author(s):  
Yi Huang ◽  
Sanshan Tu ◽  
Hongqi Yang ◽  
Leilei Dong
Keyword(s):  
Complex Variable ◽  
Meshless Method ◽  
Kriging Interpolation ◽  
Element Free Galerkin Method ◽  
Moving Kriging Interpolation ◽  
Element Free Galerkin ◽  
Domain Type ◽  
Potential Problems ◽  
Low Efficiency ◽  
Element Free

The moving Kriging interpolation (MKI) is an accurate approximation method that has the interpolating property. However, it is rarely used in meshless methods because of its low efficiency. In this paper, we proposed an efficient MKI method, the complex variable moving Kriging interpolation (CVMKI) method, for “domain” type meshless method. Further, we proposed the CVMKI-based element-free Galerkin (CVMKIEFG) method for 2D potential problems. CVMKIEFG is an efficient meshless method and can impose the essential boundary conditions directly and easily. We proposed two formulations for CVMKIEFG: the conventional formulation and the cell-based formulation. The latter formulation is proposed for higher efficiency. Three 2D example problems are presented to demonstrate the efficiency and accuracy of CVMKIEFG.

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.

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.

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