scholarly journals Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan ◽  
Mahmoud A. Zaky ◽  
Ahmed S. Hendy
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Element Free Galerkin Method ◽  
Neutral Delay ◽  
Diffusion Wave ◽  
Element Free Galerkin ◽  
Numerical Formulation ◽  
Element Free

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

scholarly journals Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

2020 ◽  
Vol 42 (4) ◽  
pp. 415-426
Author(s):  
Canh V. Le ◽  
Phuc L. H. Ho
Keyword(s):  
Optimization Problem ◽  
Shape Function ◽  
Limit State ◽  
Great Accuracy ◽  
Homogenization Theory ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Second Order Cone ◽  
Numerical Formulation ◽  
Element Free

This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.

scholarly journals The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution

2012 ◽  
Vol 16 (2) ◽  
pp. 385-394 ◽  
Author(s):  
V.D. Beibalaev ◽  
R.P. Meilanov
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Fractional Derivative ◽  
Monte Carlo Methods ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Difference Problem ◽  
The Stability

A finite difference approximation for the Caputo fractional derivative of the 4-?, 1 < ? ? 2 order has been developed. A difference schemes for solving the Dirihlet?s problem of the Poisson?s equation with fractional derivatives has been applied and solved. Both the stability of difference problem in its right-side part and the convergence have been proved. A numerical example was developed by applying both the Liebman and the Monte-Carlo methods.

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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