scholarly journals A finite point algorithm for soil water-salt movement equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fenhong Li ◽  
Gang Hu ◽  
Thabet Abdeljawad ◽  
Muhammad Abbas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soil Water ◽  
Point Method ◽  
Square Function ◽  
Finite Point ◽  
Moving Least Square ◽  
Finite Point Method ◽  
Water Salt ◽  
Element Method

AbstractIn this paper, we propose the meshless finite point method for solving a type of fluid flow problem. The moving least square function is combined with the collocation method to treat nonlinear one- and two-dimensional soil water-salt movement equations. An adaptive windward scheme is used to stabilize the numerical solution in regions with a large gradient change. Numerical examples with the comparison among the proposed method, finite element method and characteristic finite element method show that the meshless finite point method is more accurate and is used to eliminate the numerical oscillation phenomenon.

Two Implicit Meshless Finite Point Schemes for the Two-Dimensional Distributed-Order Fractional Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 813-831
Author(s):  
Rezvan Salehi
Keyword(s):  
Reproducing Kernel ◽  
Point Method ◽  
Least Square ◽  
Computationally Efficient ◽  
Finite Point ◽  
Moving Least Square ◽  
Point Collocation ◽  
Finite Point Method ◽  
Distributed Order ◽  
Fractional Equation

AbstractIn this paper, the distributed-order time fractional sub-diffusion equation on the bounded domains is studied by using the finite-point-type meshless method. The finite point method is a point collocation based method which is truly meshless and computationally efficient. To construct the shape functions of the finite point method, the moving least square reproducing kernel approximation is employed. Two implicit discretisation of order{O(\tau)}and{O(\tau^{1+\frac{1}{2}\sigma})}are derived, respectively. Stability and{L^{2}}norm convergence of the obtained difference schemes are proved. Numerical examples are provided to confirm the theoretical results.

2D Meshless Solution of Elastoplastic with Damage Problem

2012 ◽  
Vol 504-506 ◽  
pp. 413-418 ◽  
Author(s):  
Zohra Sendi ◽  
Carl Labergère ◽  
Khemais Saanouni ◽  
Hedi Belhadj Salah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computing Time ◽  
Least Square ◽  
Ductile Damage ◽  
Isotropic Hardening ◽  
The Finite Element Method ◽  
Time Step ◽  
Moving Least Square ◽  
Element Method

The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive remeshing is often the proposed solution in this case. But the remeshing raises the problems of precision and computing time. In this context and in order to avoid the remeshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.

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