scholarly journals Numerical solution of potential problems using radial basis reproducing kernel particle method

2019 ◽  
Vol 13 ◽  
pp. 102122 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Numerical Solution ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Potential Problems ◽  
Radial Basis ◽  
Reproducing Kernel Particle

The Meshless Method for Numerical Solution of Modified Equal Width Wave (MEW) Equation

2011 ◽  
Vol 101-102 ◽  
pp. 1130-1133
Author(s):  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Variational Method ◽  
Numerical Solution ◽  
Meshless Method ◽  
Penalty Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Numerical Examples ◽  
Discrete Equations ◽  
Reproducing Kernel Particle

The reproducing kernel particle method (RKPM) is used in this paper to find the numerical solution of modified equal width wave (MEW) equation. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. The effectiveness of the RKPM for the modified equal width equation is investigated by two numerical examples in this paper.

Meshless Method for the Numerical Solution of a Kind of Linear Hyperbolic Equations

2011 ◽  
Vol 101-102 ◽  
pp. 586-590
Author(s):  
Hai Na Sun ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Numerical Solution ◽  
Reproducing Kernel ◽  
Hyperbolic Equations ◽  
Particle Method ◽  
Two Dimensional ◽  
Reproducing Kernel Particle Method ◽  
Hyperbolic Problems ◽  
Linear Hyperbolic Equation ◽  
Discrete Equations ◽  
Reproducing Kernel Particle

The present paper deals with the numerical solution of two-dimensional linear hyperbolic equation using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations and the essential boundary conditions that are enforced by the penalty method. The effectiveness RKPM for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.

The Meshfree Analysis of Geometrically Nonlinear Problem Based on Radial Basis Reproducing Kernel Particle Method

2020 ◽  
Vol 12 (04) ◽  
pp. 2050044 ◽  
Author(s):  
Zheng Liu ◽  
Gaofeng Wei ◽  
Zhiming Wang ◽  
Jinwei Qiao
Keyword(s):  
Nonlinear Problem ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Kernel Functions ◽  
Geometrically Nonlinear ◽  
Reproducing Kernel Particle Method ◽  
Computational Accuracy ◽  
Penalty Factor ◽  
Radial Basis ◽  
Reproducing Kernel Particle

Based on the reproducing kernel particle method (RKPM) and the radial basis function (RBF), the radial basis reproducing kernel particle method (RRKPM) is presented for solving geometrically nonlinear problems. The advantages of the presented method are that it can eliminate the negative effect of diverse kernel functions on the computational accuracy and has greater computational accuracy and better convergence than the RKPM. Using the weak form of Galerkin integration and the Total Lagrangian (T.L.) formulation, the correlation formulae of the RRKPM for geometrically nonlinear problem are obtained. Newton–Raphson (N-R) iterative method is utilized in the process of numerical solution. Moreover, penalty factor, the scaling parameter, the shaped parameter of the RBF and loading step number are discussed. To prove validity of the proposed method, several numerical examples are simulated and compared to finite element method (FEM) solutions.

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