scholarly journals A meshless Galerkin method for Dirichlet problems using radial basis functions

2006 ◽  
Vol 196 (2) ◽  
pp. 394-401 ◽  
Author(s):  
Yong Duan ◽  
Yong-Ji Tan
Keyword(s):  
Galerkin Method ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Dirichlet Problems ◽  
Radial Basis ◽  
Meshless Galerkin Method

Mixed-Mode Stress Intensity Factors by Mesh Free Galerkin Method

2009 ◽  
Vol 417-418 ◽  
pp. 957-960
Author(s):  
P.H. Wen ◽  
M.H. Aliabadi
Keyword(s):  
Stress Intensity ◽  
Galerkin Method ◽  
Radial Basis Functions ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Basis Functions ◽  
Intensity Factors ◽  
Mesh Free ◽  
Radial Basis ◽  
Mode Stress

An element-free Galerkin method is developed using radial basis interpolation functions to evaluate static and dynamic mixed-mode stress intensity factors. For dynamic problems, the Laplace transform technique is used to transform the time domain problem to frequency domain. The so-called enriched radial basis functions are introduced to accurately capture the singularity of stress at crack tip. The accuracy and convergence of mesh free Galerkin method with enriched radial basis functions for the two-dimensional static and dynamic fracture mechanics are demonstrated through several benchmark examples. Comparisons have been made with benchmarks and solutions obtained by the boundary element method.

scholarly journals Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Maryam Sarboland ◽  
Azim Aminataei
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Radial Basis Functions ◽  
Taylor Series Expansion ◽  
Time Discretization ◽  
Basis Functions ◽  
One Dimensional ◽  
Radial Basis ◽  
The One ◽  
Rms Errors

During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional nonlinear Burger equation. In this method, the trial space is generated by the multiquadric (MQ) RBF and the test space is generated by the compactly supported RBF. In the time discretization of the equation, the Taylor series expansion is used. This method is applied on some test experiments, and the numerical results have been compared with the exact solutions. The , , and root-mean-square (RMS) errors in the solutions show the efficiency and the accuracy of the method.

Evaluation of mixed-mode stress intensity factors by the mesh-free Galerkin method: Static and dynamic

2009 ◽  
Vol 44 (4) ◽  
pp. 273-286 ◽  
Author(s):  
P H Wen ◽  
M H Aliabadi
Keyword(s):  
Stress Intensity ◽  
Galerkin Method ◽  
Radial Basis Functions ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Basis Functions ◽  
Intensity Factors ◽  
Mesh Free ◽  
Radial Basis ◽  
Mode Stress

Based on the variational principle of the potential energy, the element-free Galerkin method is developed using radial basis interpolation functions to evaluate static and dynamic mixed-mode stress intensity factors. For dynamic problems, the Laplace transform technique is used to transform the time domain problem to the frequency domain. The so-called enriched radial basis functions are introduced to capture accurately the singularity of stress at crack tip. In this approach, connectivity of the mesh in the domain or integrations with fundamental or particular solutions are not required. The accuracy and convergence of the mesh-free Galerkin method with enriched radial basis functions for the two-dimensional static and dynamic fracture mechanics are demonstrated through several benchmark examples. Comparisons have been made with benchmarks and solutions obtained by the boundary element method.

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