The Improved Interpolating Complex Variable Element Free Galerkin Method for Two-Dimensional Potential Problems

2019 ◽  
Vol 11 (10) ◽  
pp. 1950104 ◽  
Author(s):  
Yajie Deng ◽  
Xiaoqiao He ◽  
Ying Dai
Keyword(s):  
Complex Variable ◽  
Basis Function ◽  
Potential Problem ◽  
Shape Function ◽  
Weak Form ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Potential Problems ◽  
Element Free

In this paper, the improved interpolating complex variable moving least squares (IICVMLS) method is applied, in which the complete basis function is introduced and combined with the singular weight function to achieve the orthometric basis function. Then, the interpolating shape function is achieved to construct the interpolating trial function. Incorporating the IICVMLS method and the Galerkin integral weak form, an improved interpolating complex variable element free Galerkin (IICVEFG) method is proposed to solve the 2D potential problem. Because the essential boundary conditions can be straightaway imposed in the above method, the expressions of final dispersed matrices are more concise in contrast to the non-interpolating complex variable meshless methods. Through analyzing four specific potential problems, the IICVEFG method is validated with greater computing precision and efficiency.

A NEW ELEMENT-FREE GALERKIN METHOD BASED ON IMPROVED COMPLEX VARIABLE MOVING LEAST-SQUARES APPROXIMATION FOR ELASTICITY

2012 ◽  
Vol 01 (01) ◽  
pp. 1250011 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Complex Variable ◽  
Weak Form ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Elasticity Problems ◽  
Element Free

In this paper, by constructing a new functional, an improved complex variable moving least-squares (ICVMLS) approximation is presented. Based on element-free Galerkin (EFG) method and the ICVMLS approximation, a new complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented. Galerkin weak form is used to obtain the discretized equations and the essential boundary conditions are applied with Lagrange multiplier. Then the formulae of the new CVEFG method for two-dimensional elasticity problems are obtained. Compared with the conventional EFG method, the new CVEFG method has greater computational precision and efficiency. For the purposes of demonstration, some selected numerical examples are solved using the ICVEFG method.

An Improved Interpolating Complex Variable Meshless Method for Bending Problem of Kirchhoff Plates

2017 ◽  
Vol 09 (06) ◽  
pp. 1750089 ◽  
Author(s):  
Yajie Deng ◽  
Xiaoqiao He
Keyword(s):  
Complex Variable ◽  
Basis Function ◽  
Meshless Method ◽  
Shape Function ◽  
Galerkin Methods ◽  
Kirchhoff Plates ◽  
Element Free Galerkin ◽  
Variable Element ◽  
Element Free ◽  
Methods Numerical

An improved interpolating complex variable moving least squares (IICVMLS) method is proposed for numerical simulations of structures, in which a complete basis function and singular weight function are used to form a new basis function through the orthogonalization process. In this method, a new shape function which has the property of Kronecker [Formula: see text] function is derived to build the interpolating function. Based on the IICVMLS method, an improved interpolating complex variable element free Galerkin (IICVEFG) method is obtained for bending problem of Kirchhoff plates. In the IICVEFG method, the essential boundary conditions can be satisfied directly, and thus the final discrete matrix equation is more concise than that in the non-interpolating complex variable element free Galerkin methods. Hence, the proposed meshless method is more accurate and efficient than conventional complex variable meshless methods. Numerical examples of bending problem of Kirchhoff plates are presented to validate the advantages of the IICVEFG method.

The Improved Interpolating Dimension Splitting Element-Free Galerkin Method for 3D Potential Problems

2021 ◽  
Author(s):  
Zhijuan Meng ◽  
Yuye Ma ◽  
Xiaofei Chi ◽  
Lidong Ma
Keyword(s):  
Weight Function ◽  
Shape Function ◽  
Three Dimensional ◽  
Computational Accuracy ◽  
Element Free Galerkin Method ◽  
Numerical Examples ◽  
Element Free Galerkin ◽  
Potential Problems ◽  
Element Free ◽  
Better Than

This paper proposes the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on the nonsingular weight function for three-dimensional (3D) potential problems. The core of the IIDSEFG method is to transform the 3D problem domain into a series of two-dimensional (2D) problem subdomains along the splitting direction. For the 2D problems on these 2D subdomains, the shape function is constructed by the improved interpolating moving least-squares (IIMLS) method based on the nonsingular weight function, and the finite difference method (FDM) is used to couple the discretized equations in the direction of splitting. Finally, the calculation formula of the IIDSEFG method for a 3D potential problem is derived. Compared with the improved element-free Galerkin (IEFG) method, the advantages of the IIDSEFG method are that the shape function has few undetermined coefficients and the essential boundary conditions can be executed directly. The results of the selected numerical examples are compared by the IIDSEFG method, IEFG method and analytical solution. These numerical examples illustrate that the IIDSEFG method is effective to solve 3D potential problems. The computational accuracy and efficiency of the IIDSEFG method are better than the IEFG method.

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