A point interpolation meshless method based on radial basis functions

By Jian-Guo Wang, Guirong Liu. 2002

1,053 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6f7b328bbdae1cfd2c020047a8c760bb3b8a6de4

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Numerical analysis of Biot's consolidation process by radial point interpolation method (2002, background): “In order to overcome this difficulty, a radial PIM (Wang and Liu, 2001) was proposed.”
Meshfree Methods: Progress Made after 20 Years (2017, positive): “The radial point interpolation method (RPIM) (Wang and Liu 2002) uses a combination of radial and polynomial basis functions, which gives completeness, the interpolation property, and offers efficient derivative computation.”
A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions (2003, methodology): “However, when the classical RBFs are incorporated into EFG (Wendland, 1999; Wang and Liu, 2002a ) and/or MLPG (Liu and Gu, 2001b) schemes, the above-mentioned problems are removed because both EFG and MLPG perform interpolation of field variables in localized (compactly supported) domains supported”
Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter (2008, methodology): “[32–34] and by Ferreira [35–37] for composite laminated plates and beams using the first-order and the third-order shear deformation theory.”
Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation (2009, methodology): “Another meshfree method, the radial point interpolation method (RPIM), which has been developed by Wang and Liu [30, 31], has some advantages over the EFGM.”
Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method (2002, methodology): “, 1995), h p clouds (Duarte and Oden, 1996), the partition of unity (Babuska and Melenk, 1997), smooth particle hydrodynamics (Monaghan, 1988), and radial point interpolation method (Wang and Liu, 2002).”
Solving high order ordinary differential equations with radial basis function networks (2005, methodology): “In this regard, many attempts based on high order approximation schemes were made (e.g. Viecelli [3]; Sallam and El-Hawary [4]; Esmail et al [5]; Gutierrez and Laura [6]; Wu and Liu [7,8,9]).”
On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three‐dimensional wave equations (2016, methodology): “In order to avoid the singularity difficulty in the polynomial PIM, the RBF is used to develop the RPIM for meshless weak form techniques [58, 60, 61].”
Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method (2008, methodology): “The radial point interpolation meshless method (RPIM) [12,31] has been demonstrated to be an efficient meshless method and successfully applied in many engineering problems [32–36].”
Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations (2011, neutral): “The use of radial basis function for the analysis of structures and materials has been previously studied by numerous authors [27–41].”
Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations (2005, methodology): “[49–51] and by Ferreira [52–54] for composite laminated plates and beams using the first-order and the third-order shear deformation theory.”