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 An element-free Galerkin method for electromechanical coupled analysis in piezoelectric materials with cracks

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769373
Author(s):  
Xiao Lin Li ◽  
Li Ming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Piezoelectric Materials ◽  
New Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Electromechanical Coupled ◽  
Element Method

We present an element-free Galerkin method for electromechanical coupled fracture analysis in piezoelectric materials. Singularity terms were introduced into the approximation function of the new method to describe the displacement and electric fields near the crack. The new method requires a smaller domain to describe the crack-tip singular field compared with the finite element method. Then, we computed the J-integrals of piezoelectric materials and investigated the effects of crack length on the computational precision. Numerical examples were used to highlight the accuracy of the new method compared with the analytical solutions and finite element method.

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.

Element-Free Galerkin method for dynamic boundary flow problems

2020 ◽  
Vol 34 (24) ◽  
pp. 2050257
Author(s):  
Jun-Nan Meng ◽  
Guang Pan ◽  
Yong-Hui Cao
Keyword(s):  
Galerkin Method ◽  
Penalty Function Method ◽  
Element Free Galerkin Method ◽  
Navier Stokes Equation ◽  
Essential Boundary Condition ◽  
Boundary Flow ◽  
Flow Problems ◽  
Element Free Galerkin ◽  
Dynamic Boundary ◽  
Element Free

This paper focuses on the study of dynamic boundary flow problems based on the Element-Free Galerkin method. First, 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. 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. However, irregular changes in boundary conditions are often encountered in practical fluid problems. For example, the motion of flapping-foil is not uniform relative to the flow. In this paper, numerical experiments are carried out for the flow problems with non-uniform boundary motions. The problem which a plate with non-uniform drag movement above a rectangular tank filled with water is studied with the EFG method. The feasibility of the proposed algorithm is verified by comparison with the FEM method. Then, the procession of the water in the tank is stimulated. In the end, the influence of different calculation time steps on the accuracy of the solution is discussed.

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.

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