A meshless local moving Kriging method for two-dimensional solids

Zheng, Bocong; Dai, Baodong

doi:10.1016/j.amc.2011.05.100

Cited by 43 publications

(20 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Authors of [80] studied the difference between the meshfree shape functions created based on the point interpolation and the Kriging interpolation formulas. An improved meshless local Petrov-Galerkin method (MLPG) for stress analysis of two-dimensional solids is presented in [81]. As said in [81], the essential boundary conditions can be enforced similar to the FEM, no domain integration is needed and only regular boundary integration is involved.…”

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

“…An improved meshless local Petrov-Galerkin method (MLPG) for stress analysis of two-dimensional solids is presented in [81]. As said in [81], the essential boundary conditions can be enforced similar to the FEM, no domain integration is needed and only regular boundary integration is involved.…”

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

“…A meshfree boundary integral equation (BIE) method, called the moving Kriging interpolation based boundary node method (MKIBNM), is developed for solving two-dimensional potential problems in [97]. Authors of [81] investigated an improved MLPG method for stress analysis of two-dimensional solids. Authors of [98] Also we refer the interested reader to [99] where the direct MLPG (DMLPG) procedure with modified weight function in generalized MLS (GMLS) was proposed for Poisson, linearized Poisson-Boltzmann with different dielectric constants and planar elasticity problems with closed interface.…”

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach

Dehghan

Abbaszadeh

2016

Computers & Mathematics with Applications

View full text Add to dashboard Cite

Available online xxxx Keywords: Element free Galerkin (EFG) and movingKriging interpolation Fourth-order Runge-Kutta method Mathematical biology and Turing system Gray-Scott model and Allen-Cahn equation Ginzburg-Landau model and Brusselator equation Predator-prey model with additional food supply to predator a b s t r a c tIn this paper a numerical procedure is presented for solving a class of three-dimensional Turing system. First, we discrete the spatial direction using element free Galerkin (EFG) method based on the shape functions of moving Kriging interpolation. Then, to achieve a high-order accuracy, we use the fourth-order exponential time differencing Runge-Kutta (ETDRK4) method. Using this discretization for the temporal dimension, we obtain an explicit scheme and do not need to solve nonlinear system of equations. The EFG method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the EFG method test and trial functions are moving least squares approximation (MLS) shape functions. Since the shape functions of moving least squares (MLS) approximation do not have Kronecker delta property, we cannot implement the essential boundary condition, directly. Also building shape functions of MLS approximation is a time consuming procedure. Because of the mentioned reasons we employ the shape functions of moving Kriging interpolation technique which have the mentioned property and less CPU time is required for building them. For testing this method on threedimensional PDEs, we select some equations and system of PDEs such as Allen-Cahn, Gray-Scott, Ginzburg-Landau, Brusselator models, predator-prey model with additional food supply to predator. Several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme.

show abstract

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

Section: A Brief Review For Element Free Galerkin (Efg)mentioning

confidence: 99%

See 1 more Smart Citation

Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach

Dehghan

Abbaszadeh

2016

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…The element-free or mesh-free methods have been extensively researched because of its important application for solving mathematical and physical problems [1][2][3][4][5][6][7][8][9][10]; especially when the traditional computational methods are not well suited for such problems that involved extremely large deformation, dynamic fracturing or explosion problems [11]. Based on different approximation functions, various element-free or mesh-free methods were proposed, including the element-free Galerkin method [12], the hp clouds method [13], the moving least-squares differential quadrature method [14,15], the reproducing kernel particle method [16], wavelet particle method [17], the radial point interpolation method [18][19][20], the complex variable meshless method [21,22] and the meshless boundary integral equation methods [23,24].…”

Section: Introductionmentioning

confidence: 99%

An improved moving least-squares Ritz method for two-dimensional elasticity problems

Zhang

Liew

2014

Applied Mathematics and Computation

View full text Add to dashboard Cite

“…Shape functions are based on a set of nodes and a certain weight function with a local support associated with each of these nodes. Therefore, they can solve many engineering problems that are not suited to the conventional computational methods [17,47,53]. Bhrawy et al [10] reported a new spectral collocation technique for solving second kind Fredholm integral equations (FIEs).…”

Section: Introductionmentioning

confidence: 99%

Universal approximation method for the solution of integral equations

Otadi

Mosleh

2017

Math Sci

View full text Add to dashboard Cite

In this paper, we present a novel approach for approximating Hammerstein-Volterra delay integral equations (HVDIEs) by applying the universal approximation method through an artificial intelligence utility in a simple way. In this paper, neural network model (NNM) is applied as universal approximators for any nonlinear continuous functions. Here, neural network is considered as a part of large field called neural computing or soft computing. With this capability, the solution of HammersteinVolterra delay integral equation can be approximated by the appropriate NNM within an arbitrary accuracy.

show abstract

A meshless local moving Kriging method for two-dimensional solids

Cited by 43 publications

References 26 publications

Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach

Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach

An improved moving least-squares Ritz method for two-dimensional elasticity problems

Universal approximation method for the solution of integral equations

Contact Info

Product

Resources

About