Kernel-Based Meshless Collocation Methods for Solving Coupled Bulk–Surface Partial Differential Equations

2019 ◽  
Vol 81 (1) ◽  
pp. 375-391
Author(s):  
Meng Chen ◽  
Leevan Ling
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Methods ◽  
Partial Differential ◽  
Bulk Surface ◽  
Meshless Collocation ◽  
Surface Partial Differential Equations

The Over-Range Collocation Method for Nonlinear Analyses

2013 ◽  
Vol 300-301 ◽  
pp. 942-949
Author(s):  
Yong Ming Guo ◽  
Shunpei Kamitani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Collocation Method ◽  
Meshless Method ◽  
Collocation Methods ◽  
Nonlinear Analyses ◽  
Partial Differential ◽  
Boundary Points ◽  
Collocation Points

In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.

scholarly journals Numerical Simulation of Partial Differential Equations via Local Meshless Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 257 ◽  
Author(s):  
Imtiaz Ahmad ◽  
Muhammad Riaz ◽  
Muhammad Ayaz ◽  
Muhammad Arif ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Meshless Method ◽  
Three Dimensional ◽  
Salient Feature ◽  
Test Problems ◽  
Spatial Discretization ◽  
Partial Differential ◽  
Meshless Collocation

In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain and also far less sensitive to the variation of shape parameter as compared to the global meshless method (GMM). Both rectangular and non rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy and ease implementation of the proposed method are shown via test problems.

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