A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels

A new spectral meshless radial point interpolation (SMRPI) method: A well-behaved alternative to the meshless weak forms

“…In the current work, we have chosen the thin plate spline (TPS) as radial basis functions in Eq. (6). This RBF is defined as follows:…”

“…There are three kinds of meshless methods: meshless methods based on weak forms such as the element free Galerkin (EFG) method (and its developments like for example improved EFG (IEFG), complex variable (EFG) (CVEFG) and improved complex variable (EFG) (ICVEFG)), meshless local Petrov-Galerkin (MLPG) method [4][5][6][7][8][9][10] and MLPG based on the particular solutions (MLPG-PS), meshless techniques based on collocation techniques (strong forms) such as the meshless collocation technique based on radial basis functions (RBFs) [11][12][13][14][15][16][17][18][19] and the method of approximate particular solutions (MAPS) [20] and finally meshless techniques based on the combination of weak forms and collocation technique [21][22][23][24][25][26]. Due to the ill-conditioning of the resultant linear systems in RBF-collocation method, various approaches such as some regularization methods are proposed to overcome this difficulty, Refs.…”

Calculating the single-domain heat conduction with heat source problem by virtual boundary meshfree Galerkin method

“…Dehghan et al calculated the transient heat conduction in continuously nonhomogeneous functionally graded materials by using the meshfree local boundary integral equation [12]. Simultaneously, they analyzed other problems [13][14][15][16][17] by BEM or the meshfree method. Combining VBEM and the meshfree method and simultaneously employing the Galerkin method of the weighted residual methods, the equation of the virtual boundary meshfree Galerkin method (VBMGM) for the single-domain heat conduction with heat source problem can be formed.…”

A meshless local discrete collocation (MLDC) scheme for solving 2‐dimensional singular integral equations with logarithmic kernels

“…The MLS methodology as a local meshless method has been used for solving linear and nonlinear integral equations on 2‐dimensional domains() and integro‐differential equations . The paper has described a computational method for solving Fredholm integral equations with logarithmic kernels so‐called the meshless discrete Galerkin method. Li and Zhu and Assari and Dehghan have introduced a MLS‐based meshless Galerkin method for numerically solving boundary integral equations and obtained an error bound …”