scholarly journals New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem

2011 ◽  
Vol 6 ◽  
pp. 2401089-2401089
Author(s):  
Ayumu SAITOH ◽  
Taku ITOH ◽  
Nobuyuki MATSUI ◽  
Atsushi KAMITANI ◽  
Hiroaki NAKAMURA
Keyword(s):  
Boundary Condition ◽  
Galerkin Method ◽  
Nonlinear Problem ◽  
Element Free Galerkin Method ◽  
Essential Boundary Condition ◽  
Element Free Galerkin ◽  
Implementation Method ◽  
Element Free ◽  
Extended Element

Application of Extended Element-Free Galerkin Method to Nonlinear Problem

2012 ◽  
Vol 48 (2) ◽  
pp. 487-490 ◽  
Author(s):  
Ayumu Saitoh ◽  
Taku Itoh ◽  
Nobuyuki Matsui ◽  
Atsushi Kamitani
Keyword(s):  
Galerkin Method ◽  
Nonlinear Problem ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Extended Element

New Method for Implementing Essential Boundary Condition to Element-Free Galerkin Method

2010 ◽  
Author(s):  
Ayumu Saitoh ◽  
Taku Itoh ◽  
Nobuyuki Matsui ◽  
Atsushi Kamitani ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Galerkin Method ◽  
New Method ◽  
Element Free Galerkin Method ◽  
Essential Boundary Condition ◽  
Element Free Galerkin ◽  
Element Free

An Improved Element-Free Galerkin Method for a Kind of KdV Equations

2011 ◽  
Vol 101-102 ◽  
pp. 471-474
Author(s):  
Feng Xin Sun ◽  
Ju Feng Wang
Keyword(s):  
Galerkin Method ◽  
Kdv Equation ◽  
Delta Function ◽  
Element Free Galerkin Method ◽  
Essential Boundary Condition ◽  
Discrete Equations ◽  
Element Free Galerkin ◽  
Numerical Effort ◽  
The Galerkin Method ◽  
Element Free

An improved element-free Galerkin method is presented for the numerical solution of the third-order nonlinear KdV equation by coupling the interpolating moving least-squares (IMLS) method with the Galerkin method. The shape function of the IMLS method satisfies the property of Kronecker Delta function, and then the essential boundary condition can be applied directly and easily without any additional numerical effort. A variational method is used to obtain the discrete equations. A numerical example is given to demonstrate the effectiveness of the method presented in this paper for KdV equation.

scholarly journals Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method

2019 ◽  
Vol 37 (1) ◽  
pp. 70-79
Author(s):  
Junnan Meng ◽  
Guang Pan ◽  
Yonghui Cao ◽  
Linfeng Li ◽  
Zhencen Li ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Flow Problem ◽  
Rectangular Domain ◽  
Nonlinear Flow ◽  
Penalty Function Method ◽  
Element Free Galerkin Method ◽  
Navier Stokes Equation ◽  
Essential Boundary Condition ◽  
Element Free Galerkin ◽  
Element Free

This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated.

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