Comparisons of two meshfree local point interpolation methods for structural analyses

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A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions (2003, background): “Recently, radial basis functions (RBFs) (Hardy, 1971) have been popularly employed in solving partial differential equations (Kansa, 1990; Golberg et al., 1996; Fasshauer, 1997) and meshless methods (Wendland, 1999; Liu and Gu, 2001b; Liu and Gu, 2002; Wang and Liu, 2002a; Atluri and Shen, 2002), ”
Assessment and applications of point interpolation methods for computational mechanics (2004, methodology): “The detailed studies of performance and efficiency of local meshfree methods please refer to papers by Liu and Gu [18].”
An implicit RBF meshless approach for time fractional diffusion equations (2011, methodology): “This category of meshless methods includes the element-free Galerkin (EFG) method [20], the reproducing kernel particle method (RKPM)[21], and the point interpolation method (PIM) [22,23], the meshless local Petrov-Galerkin (MLPG) method [24], the local radial point interpolation method (LRPIM) [25,”
Time‐dependent fractional advection–diffusion equations by an implicit MLS meshless method (2011, methodology): “This category of meshless methods includes the diffuse element method (DEM) [25], the elementfree Galerkin (EFG) method [21], the reproducing kernel particle method [26], and the point interpolation method (PIM) [27, 28], the meshless local Petrov–Galerkin (MLPG) method [29], the local radial point ”