The solution of nonlinear Green–Naghdi equation arising in water sciences via a meshless method which combines moving kriging interpolation shape functions with the weighted essentially non–oscillatory method

2019 ◽  
Vol 68 ◽  
pp. 220-239 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh
Keyword(s):  
Meshless Method ◽  
Kriging Interpolation ◽  
Shape Functions ◽  
Moving Kriging Interpolation

A MOVING KRIGING INTERPOLATION-BASED MESHLESS LOCAL PETROV–GALERKIN METHOD FOR ELASTODYNAMIC ANALYSIS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350011 ◽  
Author(s):  
BAODONG DAI ◽  
JING CHENG ◽  
BAOJING ZHENG
Keyword(s):  
Galerkin Method ◽  
Present Method ◽  
Time Integration ◽  
Weak Form ◽  
Kriging Interpolation ◽  
Special Treatment ◽  
Integration Scheme ◽  
Shape Functions ◽  
Heaviside Step Function ◽  
Moving Kriging Interpolation

A meshless local Petrov–Galerkin method (MLPG) based on the moving Kriging interpolation for elastodynamic analysis is presented in this paper. The present method is developed based on the moving Kriging interpolation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each subdomain to avoid the need for domain integral in symmetric weak form. Since the shape functions constructed by this moving Kriging interpolation have the delta function property, the essential boundary conditions can be implemented easily, and no special treatment techniques are required. The discrete equations of the governing elastodynamic equations for two-dimensional solids are obtained using the local weak-forms. The Newmark method is adopted for the time integration scheme. Some numerical results are compared to that obtained from the exact solutions of the problem and other (meshless) methods. This comparison illustrates the efficiency and accuracy of the present method for solving the static and dynamic problems.

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.

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